Survey on gradient estimates for nonlinear elliptic equations in various function spaces

Byun, S.-S.; Palagachev, D.; Softova, L.

doi:10.1090/spmj/1605

Survey on gradient estimates for nonlinear elliptic equations in various function spaces
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by S.-S. Byun, D. K. Palagachev and L. G. Softova

St. Petersburg Math. J. 31 (2020), 401-419

DOI: https://doi.org/10.1090/spmj/1605

Published electronically: April 30, 2020

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Abstract:

Very general nonvariational elliptic equations of $p$-Laplacian type are treated. An optimal Calderón–Zygmund theory is developed for such a nonlinear elliptic equation in divergence form in the setting of various function spaces including Lebesgue spaces, Orlicz spaces, weighted Orlicz spaces, and variable exponent Lebesgue spaces. The addressed arguments also apply to Morrey spaces, Lorentz spaces and generalized Orlicz spaces.

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