A priori bounds for weak solutions to elliptic equations with nonstandard growth

TL;DR

This paper establishes global a priori bounds for weak solutions to elliptic equations with nonstandard growth and nonlinear boundary conditions, using localization and De Giorgi's iteration techniques.

Contribution

It introduces new a priori bounds for elliptic equations with nonstandard growth and nonlinear boundary conditions, expanding existing theoretical frameworks.

Findings

Derived global bounds for weak solutions

Applied localization and De Giorgi's iteration methods

Extended analysis to nonstandard growth conditions

Abstract

In this paper we study elliptic equations with a nonlinear conormal derivative boundary condition involving nonstandard growth terms. By means of the localization method and De Giorgi's iteration technique we derive global a priori bounds for weak solutions of such problems.