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arXiv · 2202.05414

Gradient estimates of very weak solutions to general quasilinear elliptic equations

Sun-Sig Byun·Minkyu Lim
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Abstract

We establish a gradient estimate for a very weak solution to a quasilinear elliptic equation with a nonstandard growth condition, which is a natural generalization of the $p$-Laplace equation. We investigate the maximum extent for the gradient estimate to hold without imposing any regularity assumption on the nonlinearity other than basic structure assumptions. Our results also include a higher integrability result of the gradient and the existence for the very weak solutions to such nonlinear problems.

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Sun-Sig Byun, Minkyu Lim. 2022-02-11. Gradient estimates of very weak solutions to general quasilinear elliptic equations. https://arxiv.org/abs/2202.05414

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