TY - JOUR
T1 - Gradient Bounds and Rigidity Results for Singular, Degenerate, Anisotropic Partial Differential Equations
AU - Cozzi, Matteo
AU - Farina, Alberto
AU - Valdinoci, Enrico
PY - 2014/10
Y1 - 2014/10
N2 - We consider the Wulff-type energy functional, (Formula Presented.) where B is positive, monotone and convex, and H is positive homogeneous of degree 1. The critical points of this functional satisfy a possibly singular or degenerate quasilinear equation in an anisotropic medium. We prove that the gradient of the solution is bounded at any point by the potential F(u) and we deduce several rigidity and symmetry properties.
AB - We consider the Wulff-type energy functional, (Formula Presented.) where B is positive, monotone and convex, and H is positive homogeneous of degree 1. The critical points of this functional satisfy a possibly singular or degenerate quasilinear equation in an anisotropic medium. We prove that the gradient of the solution is bounded at any point by the potential F(u) and we deduce several rigidity and symmetry properties.
UR - http://www.scopus.com/inward/record.url?scp=84904473540&partnerID=8YFLogxK
U2 - 10.1007/s00220-014-2107-9
DO - 10.1007/s00220-014-2107-9
M3 - Article
AN - SCOPUS:84904473540
VL - 331
SP - 189
EP - 214
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
SN - 0010-3616
IS - 1
ER -