Sharp exponents and a Wiener type condition for boundary regularity of quasiminimizers

TL;DR

This paper establishes a dimension-independent Wiener type condition with sharp exponents that guarantees boundary regularity of quasiminimizers of the p-energy integral, advancing understanding in nonlinear potential theory.

Contribution

The paper introduces a new Wiener type sum condition with explicit, sharp exponents for boundary regularity of quasiminimizers, independent of dimension.

Findings

Derived a sufficient Wiener type condition for boundary regularity

Explicitly expressed the exponent in terms of p and the quasiminimizing constant

Provided an example demonstrating the sharpness of the exponent

Abstract

We obtain a sufficient condition for boundary regularity of quasiminimizers of the p-energy integral in terms of a Wiener type sum of power type. The exponent in the sum is independent of the dimension and is explicitly expressed in terms of p and the quasiminimizing constant. We also show by an example that the exponent is sharp in a certain sense.