Lipschitz continuity for energy integrals with variable exponents
Michela Eleuteri, Paolo Marcellini, Elvira Mascolo · Rendiconti Lincei Matematica e Applicazioni · 2016
A regularity result for integrals of the Calculus of Variations with variable exponents is presented. Precisely, we prove that any vector-valued minimizer of an energy integral over an open set \Omega \subset \mathbb R^n , with variable exponent p(x) in the Sobolev class W^{1,r}_\mathrm {loc} (\Omega) for some r > n , is locally Lipschitz continuous in \Omega and an a priori estimate holds.