Minimizing cones for fractional capillarity problems

Serena Dipierro; Francesco Maggi; Enrico Valdinoci

doi:10.4171/RMI/1289

Minimizing cones for fractional capillarity problems

Serena Dipierro, Francesco Maggi, Enrico Valdinoci

Mathematics and Statistics

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

3 Citations (Scopus)

Abstract

We consider a fractional version of Gauß capillarity energy. A suitable extension problem is introduced to derive a boundary monotonicity formula for local minimizers of this fractional capillarity energy. As a consequence, blow-up limits of local minimizers are shown to subsequentially converge to minimizing cones. Finally, we show that in the planar case there is only one possible fractional minimizing cone, the one determined by the fractional version of Young's law.

Original language	English
Pages (from-to)	635-658
Number of pages	24
Journal	Revista Matematica Iberoamericana
Volume	38
Issue number	2
DOIs	https://doi.org/10.4171/RMI/1289
Publication status	Published - 2022

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10.4171/RMI/1289Licence: CC BY

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title = "Minimizing cones for fractional capillarity problems",

abstract = "We consider a fractional version of Gau{\ss} capillarity energy. A suitable extension problem is introduced to derive a boundary monotonicity formula for local minimizers of this fractional capillarity energy. As a consequence, blow-up limits of local minimizers are shown to subsequentially converge to minimizing cones. Finally, we show that in the planar case there is only one possible fractional minimizing cone, the one determined by the fractional version of Young's law. ",

keywords = "Capillarity problems, classification, extension methods, monotonicty formulae, nonlocal perimeter",

author = "Serena Dipierro and Francesco Maggi and Enrico Valdinoci",

note = "Funding Information: The first author is supported by the Australian Research Council DECRA DE180100957 {"}PDEs, free boundaries and applications{"}. The second author is supported by the NSF Grant DMS 2000034. The third author is supported by the Australian Laureate Fellowship FL190100081 {"}Minimal surfaces, free boundaries and partial differential equations{"}. The first and third authors are members of INdAM and AustMS Funding Information: Funding. The first author is supported by the Australian Research Council DECRA DE-180100957 “PDEs, free boundaries and applications”. The second author is supported by the NSF Grant DMS 2000034. The third author is supported by the Australian Laureate Fellowship FL190100081 “Minimal surfaces, free boundaries and partial differential equations”. The first and third authors are members of INdAM and AustMS. Publisher Copyright: {\textcopyright} 2021 Real Sociedad Matem{\'a}tica Espa{\~n}ola.",

year = "2022",

doi = "10.4171/RMI/1289",

language = "English",

volume = "38",

pages = "635--658",

journal = "Revista Matematica Iberoamericana",

issn = "0213-2230",

publisher = "Universidad Autonoma de Madrid",

number = "2",

}

TY - JOUR

T1 - Minimizing cones for fractional capillarity problems

AU - Dipierro, Serena

AU - Maggi, Francesco

AU - Valdinoci, Enrico

N1 - Funding Information: The first author is supported by the Australian Research Council DECRA DE180100957 "PDEs, free boundaries and applications". The second author is supported by the NSF Grant DMS 2000034. The third author is supported by the Australian Laureate Fellowship FL190100081 "Minimal surfaces, free boundaries and partial differential equations". The first and third authors are members of INdAM and AustMS Funding Information: Funding. The first author is supported by the Australian Research Council DECRA DE-180100957 “PDEs, free boundaries and applications”. The second author is supported by the NSF Grant DMS 2000034. The third author is supported by the Australian Laureate Fellowship FL190100081 “Minimal surfaces, free boundaries and partial differential equations”. The first and third authors are members of INdAM and AustMS. Publisher Copyright: © 2021 Real Sociedad Matemática Española.

PY - 2022

Y1 - 2022

N2 - We consider a fractional version of Gauß capillarity energy. A suitable extension problem is introduced to derive a boundary monotonicity formula for local minimizers of this fractional capillarity energy. As a consequence, blow-up limits of local minimizers are shown to subsequentially converge to minimizing cones. Finally, we show that in the planar case there is only one possible fractional minimizing cone, the one determined by the fractional version of Young's law.

AB - We consider a fractional version of Gauß capillarity energy. A suitable extension problem is introduced to derive a boundary monotonicity formula for local minimizers of this fractional capillarity energy. As a consequence, blow-up limits of local minimizers are shown to subsequentially converge to minimizing cones. Finally, we show that in the planar case there is only one possible fractional minimizing cone, the one determined by the fractional version of Young's law.

KW - Capillarity problems

KW - classification

KW - extension methods

KW - monotonicty formulae

KW - nonlocal perimeter

UR - http://www.scopus.com/inward/record.url?scp=85124787414&partnerID=8YFLogxK

U2 - 10.4171/RMI/1289

DO - 10.4171/RMI/1289

M3 - Article

AN - SCOPUS:85124787414

SN - 0213-2230

VL - 38

SP - 635

EP - 658

JO - Revista Matematica Iberoamericana

JF - Revista Matematica Iberoamericana

IS - 2

ER -

Minimizing cones for fractional capillarity problems

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Minimal surfaces, free boundaries and partial differential equations

Partial Differential Equations, free boundaries and applications

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Minimizing cones for fractional capillarity problems

Abstract

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Minimal surfaces, free boundaries and partial differential equations

Partial Differential Equations, free boundaries and applications

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