Gradient estimates for quasilinear elliptic Neumann problems with unbounded first-order terms

TL;DR

This paper establishes global gradient bounds for quasilinear elliptic equations with unbounded first-order terms and Neumann boundary conditions, under integrability assumptions on the source, extending understanding of such problems in convex domains.

Contribution

It provides new a priori gradient estimates for divergence-type equations with polynomial growth first-order terms, applicable to unbounded data in convex domains.

Findings

Derived global gradient estimates for equations with unbounded first-order terms.

Applicable to elliptic problems with unbounded data and Neumann boundary conditions.

Extended the theory to convex domains with polynomial growth conditions.

Abstract

This paper studies global a priori gradient estimates for divergence-type equations patterned over the $p$-Laplacian with first-order terms having polynomial growth with respect to the gradient, under suitable integrability assumptions on the source term of the equation. The results apply to elliptic problems with unbounded data in Lebesgue spaces complemented with Neumann boundary conditions posed on convex domains of the Euclidean space.