In this paper we establish the boundedness and the higher differentiability of solutions to the {div(A(x,Du))+b(x)|u(x)|u(x)=fin ?u=0on ?? under a Sobolev assumption on the partial map x->A(x,?). The novelty here is that we deal with degenerate elliptic operator A(x,?) with p-growth, p>=2, with respect to the gradient variable, in presence of lower order terms. The interplay between b(x) and f(x), introduced in ([1]), gives a regularizing effect also in the degenerate elliptic setting.
On the regularity of solutions to a class of degenerate PDE's with lower order terms
Capone C
2021
Abstract
In this paper we establish the boundedness and the higher differentiability of solutions to the {div(A(x,Du))+b(x)|u(x)|u(x)=fin ?u=0on ?? under a Sobolev assumption on the partial map x->A(x,?). The novelty here is that we deal with degenerate elliptic operator A(x,?) with p-growth, p>=2, with respect to the gradient variable, in presence of lower order terms. The interplay between b(x) and f(x), introduced in ([1]), gives a regularizing effect also in the degenerate elliptic setting.File in questo prodotto:
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