Sobolev regularity for nonlinear Poisson equations with Neumann boundary conditions on Riemannian manifolds-Reference-Cited by-同舟云学术

Sobolev regularity for nonlinear Poisson equations with Neumann boundary conditions on Riemannian manifolds

Published:2023-01-30 Issue:2 Volume:35 Page:431-456
ISSN:0933-7741
Container-title:Forum Mathematicum
language:en
Short-container-title:

Author:

Goffi Alessandro¹,Pediconi Francesco²^ORCID

Affiliation:

1. Dipartimento di Matematica “Tullio Levi-Civita” , Università di Padova , Via Trieste 63, 35121 Padova , Italy

2. Department of Mathematics , Aarhus University , Ny Munkegade 118, 8000 Aarhus C , Denmark

Abstract

Abstract In this paper, we study the Sobolev regularity of solutions to nonlinear second order elliptic equations with super-linear first-order terms on Riemannian manifolds, complemented with Neumann boundary conditions, when the source term of the equation belongs to a Lebesgue space, under various integrability regimes. Our method is based on an integral refinement of the Bochner identity, and leads to “semilinear Calderón–Zygmund” type results. Applications to the problem of smoothness of solutions to Mean Field Games systems with Neumann boundary conditions posed on convex domains of the Euclidean space will also be discussed.

Funder

Istituto Nazionale di Alta Matematica ”Francesco Severi”

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/forum-2022-0119/pdf

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