Survey on gradient estimates for nonlinear elliptic equations in various function spaces. (English) Zbl 1437.35283
St. Petersbg. Math. J. 31, No. 3, 401-419 (2020) and Algebra Anal. 31, No. 3, 10-35 (2019).
Summary: 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.
MSC:
| 35J60 | Nonlinear elliptic equations |
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 46E30 | Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) |
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
Keywords:
equations of \(p\)-Laplacian type; Calderón-Zygmund theory; Orlicz spaces; variable exponent Lebesgue spaces; Morrey spaces; Lorentz spacesReferences:
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