Partial Differential Equations, free boundaries and applications

Search results

• 2025

  Diffusive Processes Modeled on the Spectral Fractional Laplacian with Dirichlet Boundary Conditions

  Dipierro, S., Giacomin, G. & Valdinoci, E., 2025, Analysis and Numerics of Design, Control and Inverse Problems. Floridia, G. & Zuazua, E. (eds.). Springer-Verlag Italia s.r.l., p. 82-116 35 p. (Springer INdAM Series; vol. 63).

  Research output: Chapter in Book/Conference paper › Conference paper › peer-review

  • Diffusive 100%
  • Laplace Operator 100%
  • Neumann Boundary Condition 100%
  • Boundary Condition 100%
  • Singularities 50%

• 2024

  Lipschitz Regularity of Almost Minimizers in One-Phase Problems Driven by the p-Laplace Operator

  Dipierro, S., Ferrari, F., Forcillo, N. & Valdinoci, E., 2024, In: Indiana University Mathematics Journal. 73, 3, p. 813-854 42 p.

  Research output: Contribution to journal › Article › peer-review

  • p-Laplacian 100%

  3   Link opens in a new tab Citations (Scopus)

• Nonlocal capillarity for anisotropic kernels

  De Luca, A., Dipierro, S. & Valdinoci, E., Apr 2024, In: Mathematische Annalen. 388, 4, p. 3785-3846 62 p.

  Research output: Contribution to journal › Article › peer-review

  • Anisotropic 100%
  • Capillarity 100%
  • Scale Invariance 100%
  • Solvability 100%
  • Adhesion Coefficient 50%

  2   Link opens in a new tab Citations (Scopus)

• The Lévy Flight Foraging Hypothesis in Bounded Regions: Subordinate Brownian Motions and High-risk/High-gain Strategies

  Dipierro, S., Giacomin, G. & Valdinoci, E., 2024, 1 ed. European Mathematical Society Publishing House.

  Research output: Book/Report › Book › peer-review

  Open Access

• The role of antisymmetric functions in nonlocal equations

  Dipierro, S., Poggesi, G., Thompson, J. & Valdinoci, E., Mar 2024, In: Transactions of the American Mathematical Society. 377, 3, p. 1671-1692 22 p.

  Research output: Contribution to journal › Article › peer-review

  • Semilinear 100%
  • Dirichlet Problem 100%
  • Fractional Laplacian 100%
  • Counterexample 50%
  • Parallel Surface 50%

  5   Link opens in a new tab Citations (Web of Science)

  23 Downloads (Pure)

• 2023

  (Non)local logistic equations with Neumann conditions

  Dipierro, S., Lippi, E. P. & Valdinoci, E., 2023, In: Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire. 40, 5, p. 1093-1166 74 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Neumann Condition 100%
  • Logistic Equation 100%
  • Eigenvalue 66%
  • Asymptotics 33%
  • Positive Eigenvalue 33%

  85   Link opens in a new tab Citations (Scopus)

• (s, p)-Harmonic Approximation of Functions of Least W^s,1-Seminorm

  Bucur, C., Dipierro, S., Lombardini, L., Mazón, J. M. & Valdinoci, E., 1 Jan 2023, In: International Mathematics Research Notices. 2023, 2, p. 1173-1235 63 p.

  Research output: Contribution to journal › Article › peer-review

  • Approximation of Function 100%
  • Pointwise 100%
  • Seminorm 100%
  • Weak Solution 100%
  • Euler-Lagrange Equation 100%

  6   Link opens in a new tab Citations (Scopus)

• Classification of global solutions of a free boundary problem in the plane

  Dipierro, S., Karakhanyan, A. & Valdinoci, E., 14 Sept 2023, In: Interfaces and Free Boundaries. 25, 3, p. 455-490 36 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Global Solution 100%
  • Free Boundary Problem 100%
  • Ordinary Differential Equation 50%

  3   Link opens in a new tab Citations (Scopus)

• On the Harnack inequality for antisymmetric s-harmonic functions

  Dipierro, S., Thompson, J. & Valdinoci, E., 1 Jul 2023, In: Journal of Functional Analysis. 285, 1, 109917.

  Research output: Contribution to journal › Article › peer-review

  • Harmonic Function 100%
  • Harnack Inequality 100%
  • Overdetermined Problem 20%
  • Semilinear Equation 20%
  • Stability Result 20%

  4   Link opens in a new tab Citations (Web of Science)

• Some perspectives on (non)local phase transitions and minimal surfaces

  Dipierro, S. & Valdinoci, E., 1 Apr 2023, In: Bulletin of Mathematical Sciences. 13, 1, 77 p., 2330001.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Minimal Surface 100%

  7   Link opens in a new tab Citations (Web of Science)

• SYMMETRY AND QUANTITATIVE STABILITY FOR THE PARALLEL SURFACE FRACTIONAL TORSION PROBLEM

  Ciraolo, G., Dipierro, S., Poggesi, G., Pollastro, L. & Valdinoci, E., May 2023, In: Transactions of the American Mathematical Society. 376, 5, p. 3515-3540 26 p.

  Research output: Contribution to journal › Article › peer-review

  • Parallel Surface 100%
  • Overdetermined Problem 50%
  • Open Set 50%
  • Approximates 50%
  • Boundary Point 50%

  11   Link opens in a new tab Citations (Web of Science)

• THE STICKINESS PROPERTY FOR ANTISYMMETRIC NONLOCAL MINIMAL GRAPHS

  Baronowitz, B., Dipierro, S. & Valdinoci, E., Mar 2023, In: Discrete and Continuous Dynamical Systems. 43, 3-4, p. 1006-1025 20 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Multiplicative Constant 100%

  4   Link opens in a new tab Citations (Web of Science)

• 2022

  (Dis)connectedness of nonlocal minimal surfaces in a cylinder and a stickiness property

  Dipierro, S., Onoue, F. & Valdinoci, E., 2022, In: Proceedings of the American Mathematical Society. 150, 5, p. 2223-2237 15 p.

  Research output: Contribution to journal › Article › peer-review

  • Surface (Surface Science) 100%
  • Cylinder 100%
  • Minimizer 100%
  • Minimal Surface 100%

  5   Link opens in a new tab Citations (Scopus)

• A Hong-Krahn-Szegö inequality for mixed local and nonlocal operatorsy

  Biagi, S., Dipierro, S., Valdinoci, E. & Vecchi, E., 2022, In: Mathematics In Engineering. 5, 1

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Eigenvalue Problem 100%
  • Eigenvalue 100%
  • Nonlocal Operator 50%
  • Open Set 50%
  • Limit Case 50%

  40   Link opens in a new tab Citations (Scopus)

• Dispersive effects in a scalar nonlocal wave equation inspired by peridynamics

  Coclite, G. M., Dipierro, S., Fanizza, G., Maddalena, F. & Valdinoci, E., 3 Nov 2022, In: Nonlinearity. 35, 11, p. 5664-5713 50 p.

  Research output: Contribution to journal › Article › peer-review

  • Dispersive 100%
  • Wave Equation 100%
  • Peridynamics 100%
  • Spatial Dimension 50%
  • Functionals 50%

  14   Link opens in a new tab Citations (Scopus)

• Efficiency functionals for the Levy flight foraging hypothesis

  Dipierro, S., Giacomin, G. & Valdinoci, E., Oct 2022, In: Journal of Mathematical Biology. 85, 4, 50 p., 33.

  Research output: Contribution to journal › Article › peer-review

  • Optimal Strategy 100%
  • Optimality 100%
  • Heat Equation 100%
  • Evolution Equation 100%
  • Special Function 100%

  10   Link opens in a new tab Citations (Scopus)

• Integral operators defined “up to a polynomial”

  Dipierro, S., Dzhugan, A. & Valdinoci, E., Feb 2022, In: Fractional Calculus and Applied Analysis. 25, 1, p. 60-108 49 p.

  Research output: Contribution to journal › Article › peer-review

  • Polynomial 100%
  • Integral Operator 100%
  • Pointwise 33%
  • Dirichlet Problem 33%
  • Classical Definition 33%

  1   Link opens in a new tab Citation (Scopus)

• Linear theory for a mixed operator with Neumann conditions

  Dipierro, S., Lippi, E. P. & Valdinoci, E., 2022, In: Asymptotic Analysis. 128, 4, p. 571-594 24 p.

  Research output: Contribution to journal › Article › peer-review

  File

  • Neumann Condition 100%
  • Spectral Property 33%
  • Subsolution 33%
  • Logistic Equation 33%
  • Eigenvalue Problem 33%

  49   Link opens in a new tab Citations (Scopus)

  146 Downloads (Pure)

• Minimizing cones for fractional capillarity problems

  Dipierro, S., Maggi, F. & Valdinoci, E., 2022, In: Revista Matematica Iberoamericana. 38, 2, p. 635-658 24 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Local Minimizer 100%

  4   Link opens in a new tab Citations (Scopus)

• Mixed local and nonlocal elliptic operators: regularity and maximum principles

  Biagi, S., Dipierro, S., Valdinoci, E. & Vecchi, E., 2022, In: Communications in Partial Differential Equations. 47, 3, p. 585-629 45 p.

  Research output: Contribution to journal › Article › peer-review

  • Elliptic Operator 100%
  • Classical Solution 50%
  • Fractional Laplacian 50%
  • Laplace Operator 50%
  • Superposition 50%

  141   Link opens in a new tab Citations (Scopus)

• Non-symmetric stable operators: Regularity theory and integration by parts

  Dipierro, S., Ros-Oton, X., Serra, J. & Valdinoci, E., 4 Jun 2022, In: Advances in Mathematics. 401, 108321.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Integration by Part 100%
  • Half Space 66%
  • Fractional Laplacian 66%
  • Lvy Process 33%

  25   Link opens in a new tab Citations (Scopus)

• The Bernstein Technique for Integro-Differential Equations

  Cabré, X., Dipierro, S. & Valdinoci, E., Mar 2022, In: Archive for Rational Mechanics and Analysis. 243, 3, p. 1597-1652 56 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Extremal 100%
  • Differential Equation 100%
  • Linear Case 100%
  • Nonlinear Equation 100%
  • Open Question 100%

  32   Link opens in a new tab Citations (Scopus)

• 2021

  A Serrin-type problem with partial knowledge of the domain

  Dipierro, S., Poggesi, G. & Valdinoci, E., Jul 2021, In: Nonlinear Analysis, Theory, Methods and Applications. 208, 112330.

  Research output: Contribution to journal › Article › peer-review

  File

  • Laminar Flows 100%
  • Open Subset 100%
  • Rigidity 100%

  12   Link opens in a new tab Citations (Scopus)

  189 Downloads (Pure)

• Description of an ecological niche for a mixed local/nonlocal dispersal: An evolution equation and a new Neumann condition arising from the superposition of Brownian and Lévy processes

  Dipierro, S. & Valdinoci, E., 1 Aug 2021, In: Physica A: Statistical Mechanics and its Applications. 575, 126052.

  Research output: Contribution to journal › Article › peer-review

  File

  • Lvy Process 100%
  • Neumann Condition 100%
  • Evolution Equation 100%
  • Superposition 100%
  • Probability Theory 20%

  104   Link opens in a new tab Citations (Scopus)

  170 Downloads (Pure)

• Global gradient estimates for nonlinear parabolic operators

  Dipierro, S., Gao, Z. & Valdinoci, E., 2021, In: ESAIM - Control, Optimisation and Calculus of Variations. 27, 2021016.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Parabolic 100%
  • Riemannian Manifolds 50%
  • Ambient Space 50%
  • Parabolic Equation 50%

  3   Link opens in a new tab Citations (Scopus)

• 2020

  (Non)local γ-convergence γ-convergenza (non)locale

  Dipierro, S., Miraglio, P. & Valdinoci, E., 2020, In: Bruno Pini Mathematical Analysis Seminar. 11, 1, p. 68-93 26 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Convergence Result 100%
  • Local Convergence 100%
  • Range Interaction 100%
  • Boundary Term 100%
  • Pointwise Limit 100%

  4   Link opens in a new tab Citations (Scopus)

• A comparison between the nonlocal and the classical worlds: Minimal surfaces, phase transitions, and geometric flows

  Dipierro, S., Oct 2020, In: Notices of the American Mathematical Society. 67, 9, p. 1324-1335 12 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  4   Link opens in a new tab Citations (Scopus)

• Enhanced boundary regularity of planar nonlocal minimal graphs and a butterfly effect

  Dipierro, S., Dzhugan, A., Forcillo, N. & Valdinoci, E., 1 Jan 2020, In: Bruno Pini Mathematical Analysis Seminar. 11, 1, p. 44-67 24 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Differentiability 100%
  • Boundary Point 100%
  • Continuous Case 100%
  • Euler-Lagrange Equation 100%

  2   Link opens in a new tab Citations (Scopus)

• Improvement of flatness for nonlocal phase transitions

  Dipierro, S., Serra, J. & Valdinoci, E., Aug 2020, In: American Journal of Mathematics. 142, 4, p. 1083-1160 78 p.

  Research output: Contribution to journal › Article › peer-review

  File

  • Apply It 100%
  • Range Interaction 100%
  • De Giorgi 100%
  • Catenoid 100%
  • Critical Point 100%

  16   Link opens in a new tab Citations (Web of Science)

  83 Downloads (Pure)

• Minimisers of a fractional seminorm and nonlocal minimal surfaces

  Bucur, C., Dipierro, S., Lombardini, L. & Valdinoci, E., Dec 2020, In: Interfaces and Free Boundaries. 22, 4, p. 465-504 40 p.

  Research output: Contribution to journal › Article › peer-review

  File

  • Seminorm 100%
  • Minimal Surface 100%
  • Variational Problem 40%
  • Energy Functional 20%
  • Existence Result 20%

  10   Link opens in a new tab Citations (Scopus)

  74 Downloads (Pure)

• Nonlocal Minimal Graphs in the Plane are Generically Sticky

  Dipierro, S., Savin, O. & Valdinoci, E., Jun 2020, In: Communications in Mathematical Physics. 376, 3, p. 2005-2063 59 p.

  Research output: Contribution to journal › Article › peer-review

  • Regularity Analysis 100%

  17   Link opens in a new tab Citations (Scopus)

• Unique continuation principles in cones under nonzero Neumann boundary conditions

  Dipierro, S., Felli, V. & Valdinoci, E., 1 Jul 2020, In: Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire. 37, 4, p. 785-815 31 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Neumann Boundary Condition 100%
  • Interior Point 100%
  • Elliptic Equation 100%
  • Neumann Condition 100%
  • Forcing Term 100%

  9   Link opens in a new tab Citations (Scopus)

  69 Downloads (Pure)

• 2019

  Limit behaviour of a singular perturbation problem for the Biharmonic operator

  Dipierro, S., Karakhanyan, A. L. & Valdinoci, E., 1 Dec 2019, In: Applied Mathematics and Optimization. 80, 3, p. 679-713 35 p.

  Research output: Contribution to journal › Article › peer-review

  File

  • Singular Perturbation Problem 100%
  • Counterexample 33%
  • Free Boundary Problem 33%
  • Forcing Term 33%
  • Level Set 33%

  5   Link opens in a new tab Citations (Scopus)

  81 Downloads (Pure)