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arXiv · 2311.11479

Existence of very weak solutions to nonlinear elliptic equation with nonstandard growth and global weighted gradient estimates

Sun-Sig Byun·Minkyu Lim
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Abstract

We study a general class of quasilinear elliptic equations with nonstandard growth to prove the existence of a very weak solution to such a problem. A key ingredient in the proof is a priori global weighted gradient estimate of a very weak solution, where the right hand side of the equation is the divergence of a vector-valued function with low degree of integrability. To obtain this estimate, we adopt a notion of reverse Hölder class of Muckenhoupt weights. Another crucial part of the proof is a generalized weighted div-curl lemma in the setting of Orlicz spaces.

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Sun-Sig Byun, Minkyu Lim. 2023-11-20. Existence of very weak solutions to nonlinear elliptic equation with nonstandard growth and global weighted gradient estimates. https://arxiv.org/abs/2311.11479

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