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arXiv · 2301.08119

The double phase Dirichlet problem when the lowest exponent is equal to 1

Alexandros Matsoukas·Nikos Yannakakis
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Abstract

In this paper we prove an existence and uniqueness result for the double phase Dirichlet problem when the lowest exponent is equal to 1. Our solution is a function of bounded variation that simultaneously lies in a suitable weighted Sobolev space and is found as the limit of a sequence of solutions of intermediate double phase Dirichlet problems whose lowest exponent $p$ goes to 1. As a result of that, our approach involves the study of some relevant properties of generalized Orlicz-Sobolev spaces.

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Alexandros Matsoukas, Nikos Yannakakis. 2023-01-19. The double phase Dirichlet problem when the lowest exponent is equal to 1. https://doi.org/10.1016/j.jmaa.2023.127270

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