Linear and fully nonlinear elliptic equations with Morrey drift

DOI10.1007/S10958-022-06211-1arXiv2108.06840MaRDI QIDQ6375309

Publication date: 15 August 2021

Abstract: We present some results concerning the solvability of linear elliptic equations in bounded domains with the main coefficients almost in VMO, the drift and the free terms in Morrey classes containing

L_{d}

, and bounded zeroth order coefficient. We prove that the second-order derivatives of solutions are in a local Morrey class containing

W_{p, l o c}^{2}

. Actually, the exposition is given for fully nonlinear equations and encompasses the above mentioned results, which are new even if the main part of the equation is just the Laplacian.

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Nonlinear elliptic equations (35J60) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Existence problems for PDEs: global existence, local existence, non-existence (35A01)

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