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arXiv · 2608.08289

Conormal problem for a kind of nonlinear elliptic equations

A. F. Buscetto·R. Rescigno·L. G. Softova·S. Tramontano
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Abstract

We study the global boundedness of weak solutions to a class of nonlinear elliptic equations in bounded Lipschitz domains, subject to conormal boundary conditions. Using techniques from Morrey space theory, Adams--Mazya trace inequalities, and higher integrability properties of the gradient, we derive uniform a priori bounds for the solutions. A crucial step in our analysis is the construction of appropriate measures associated with the solution and the application of the Hartman--Stampacchia lemma, which enables us to control the solution up to the boundary of the domain.

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A. F. Buscetto, R. Rescigno, L. G. Softova, S. Tramontano. 2026-08-08. Conormal problem for a kind of nonlinear elliptic equations. https://arxiv.org/abs/2608.08289

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