Very degenerate elliptic equations under almost critical Sobolev\n regularity

2018/03/23 by Albert Clop, Raffaella Giova, Clop, Albert +5 · 1 citation
Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems

paper · pdf · doi:10.48550/arxiv.1803.08723

Abstract

We prove the local Lipschitz continuity and the higher differentiability of\nlocal minimizers of integral functionals with non autonomous integrand which is\ndegenerate convex with respect to the gradient variable. The main novelty here\nis that the results are obtained assuming that the coefficients have weak\nderivative in an almost critical Zygmund class and the datum f is assumed to\nbelong to the same Zygmund class.\n

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