We prove local Lipschitz regularity for local minimisers ofWe prove local Lipschitz regularity for local minimisers ofW-1,W-1 (Omega) (sic) v bar right arrow integral(Omega) F(Dv) dxwhere Omega subset of R-N, N >= 2 and F : R-N -> R is a quasiuniformly convex integrand in the sense of Kovalev and Maldonado (Ill J Math 49:1039-1060, 2005), i. e. a convex C-1-function such that the ratio between themaximum andminimum eigenvalues of (DF)-F-2 is essentially bounded. This class of integrands includes the standard singular/degenerate functions F(z) = vertical bar z vertical bar(p) for any p > 1 and arises as the closure, with respect to a natural convergence, of the strongly elliptic integrands of the Calculus of Variations.

Lipschitz regularity for solutions of a general class of elliptic equations

Mosconi, Sunra
2024-01-01

Abstract

We prove local Lipschitz regularity for local minimisers ofWe prove local Lipschitz regularity for local minimisers ofW-1,W-1 (Omega) (sic) v bar right arrow integral(Omega) F(Dv) dxwhere Omega subset of R-N, N >= 2 and F : R-N -> R is a quasiuniformly convex integrand in the sense of Kovalev and Maldonado (Ill J Math 49:1039-1060, 2005), i. e. a convex C-1-function such that the ratio between themaximum andminimum eigenvalues of (DF)-F-2 is essentially bounded. This class of integrands includes the standard singular/degenerate functions F(z) = vertical bar z vertical bar(p) for any p > 1 and arises as the closure, with respect to a natural convergence, of the strongly elliptic integrands of the Calculus of Variations.
2024
Calculus of Variations
Regularity
Quasiconformal mappings
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/623729
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