Regularity results for vectorial minimizers of a class of degenerate convex integrals
The authors show the higher differentiability and the higher integrability for the gradient of vectorial minimizers of integral functionals with \((p,q)\)-growth conditions. They assume that the non-homogeneous densities are uniformly convex and have a radial structure, with respect to the gradient variable, only at infinity. The results are obtained under a possibly discontinuous dependence on the spatial variable of the integrand. The main features of the energy densities are the following: \begin{itemize}\item they satisfy the so-called \((p,q)\)-growth conditions, \item they are uniformly convex only for large values of \(|\xi|\), \item the partial map \(x\mapsto f(x,\xi)\) is possibly discontinuous. \end{itemize} The study is motivated by the study of optimal transport problems with congestion effects.
non-autonomous degenerate convex functionals
scientific article; zbMATH DE number 6933418
scientific article