Nonvariational and singular double phase problems for the Baouendi-Grushin operator

TL;DR

This paper introduces a new double phase Baouendi-Grushin operator with variable coefficients, explores its properties, and proves the existence of weak solutions for related nonvariational problems, extending previous work on anisotropic integrals.

Contribution

It presents a novel nonvariational double phase Baouendi-Grushin operator, analyzes its properties, and establishes existence results for associated PDEs, expanding the theoretical framework.

Findings

Established basic properties of the new operator

Proved a compactness result for the function space

Demonstrated existence of weak solutions for nonvariational problems

Abstract

In this paper we introduce a new double phase Baouendi-Grushin type operator with variable coefficients. We give basic properties of the corresponding functions space and prove a compactness result. In the second part, using topological argument, we prove the existence of weak solutions of some nonvariational problems in which this new operator is present. The present paper extends and complements some of our previous contributions related to double phase anisotropic variational integrals.