Bounded weak solutions to elliptic PDE with data in Orlicz spaces

[摘要] A classical regularity result is that non-negative solutions to the Dirichlet problem Delta u = f in a bounded domain Omega, where f epsilon L-q (Omega), q > n/2, satisfy parallel to u parallel to(L infinity) ((Omega)) <= C parallel to f parallel to(Lq (Omega)). We extend this result in three ways: we replace the Laplacian with a degenerate elliptic operator; we show that we can take the data f in an Orlicz space L-A(Omega) that lies strictly between L-n/2 (Omega) and L-q (Omega), q > n/2; and we show that we can replace the L-A norm in the right-hand side by a smaller expression involving the logarithm of the entropy bump parallel to f parallel to(LA)(Omega)/parallel to f parallel to(Ln/2(Omega)), generalizing a result due to Xu. (C) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-10-05

[关键词] Orlicz spaces;Degenerate elliptic equations;Bounded solutions;A priori estimates