Abstract
We derive some a priori estimates and then prove the existence and regularity of distributional solutions to degenerate elliptic equations of the form
where the Carathéodory function satisfies
for , and , with a Marcinkiewicz function. We obtain a gradient estimate for entropy solutions, and show that the result is optimal by a counterexample. We also consider degenerate elliptic equations with a lower order term,
We show that the presence of the lower order term has regularizing effects on our result.
Citation
Zhang Jiaxiang. Gao Hongya. "GRADIENT ESTIMATES FOR ENTROPY SOLUTIONS TO ELLIPTIC EQUATIONS WITH DEGENERATE COERCIVITY." Rocky Mountain J. Math. 53 (1) 275 - 284, February 2023. https://doi.org/10.1216/rmj.2023.53.275
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