We prove the local Lipschitz continuity and the higher differentiability of local minimizers of functionals of the form F(u,Ω)=∫Ω(F(x,Du(x))+f(x)·u(x))dx with non-autonomous integrand F(x, ζ) which is degenerate convex with respect to the gradient variable. The main novelty here is that the results are obtained assuming that the partial map x → DξF(x,ξ)has weak derivative in the almost critical Zygmund class LnlogαL and the datum f is assumed to belong to the same Zygmund class.

Very degenerate elliptic equations under almost critical Sobolev regularity

Giova R.;
2020

Abstract

We prove the local Lipschitz continuity and the higher differentiability of local minimizers of functionals of the form F(u,Ω)=∫Ω(F(x,Du(x))+f(x)·u(x))dx with non-autonomous integrand F(x, ζ) which is degenerate convex with respect to the gradient variable. The main novelty here is that the results are obtained assuming that the partial map x → DξF(x,ξ)has weak derivative in the almost critical Zygmund class LnlogαL and the datum f is assumed to belong to the same Zygmund class.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11367/86710
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