Lipschitz regularity for minima without strict convexity of the Lagrangian |
| |
Authors: | Carlo Mariconda Giulia Treu |
| |
Institution: | aDipartimento di Matematica Pura e Applicata, Università di Padova, 63 via Trieste, I-35121 Padova, Italy |
| |
Abstract: | We give, in a non-smooth setting, some conditions under which (some of) the minimizers of among the functions in W1,1(Ω) that lie between two Lipschitz functions are Lipschitz. We weaken the usual strict convexity assumption in showing that, if just the faces of the epigraph of a convex function are bounded and the boundary datum u0 satisfies a generalization of the Bounded Slope Condition introduced by A. Cellina then the minima of on , whenever they exist, are Lipschitz. A relaxation result follows. |
| |
Keywords: | Subdifferential Convexity Strictly convex Face Epigraph Calculus of variations Lipschitz Regularity Relaxation Bounded Slope Condition Non-smooth Lavrentiev Legendre Domain Polar Demi-coercivity |
本文献已被 ScienceDirect 等数据库收录! |
|