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.
Highlights
The present paper is concerned with global a priori bounds for elliptic equations with nonlinear conormal derivative boundary conditions which may contain nonlinearities with variable growth exponents
We deal with elliptic equations of the form
In recent years there has been a growing interest in the study of elliptic problems with a p(x)-structure, which are termed problems with nonstandard growth conditions. Equations of this type appear in the study of non-Newtonian fluids with thermo-convective effects, electrorheological fluids, the
Summary
The present paper is concerned with global a priori bounds for elliptic equations with nonlinear conormal derivative boundary conditions which may contain nonlinearities with variable growth exponents. A priori estimates, De Giorgi iteration, Elliptic equations, Nonstandard growth, Partition of unity, Variable exponent spaces. A function u ∈ W 1,p(·)(Ω) is said to be a weak solution (subsolution, supersolution) of equation (1.1) if
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