We study very general nonvariational elliptic equations of $p$-Laplacian type. We discuss an optimal Calder'on--Zygmund theory of 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 apply to Morrey spaces, Lorentz spaces and generalized Orlicz spaces as well.
Survey on gradient estimates for nonlinear elliptic equations in various function spaces / Byun, S. -S.; Palagachev, D. K.; Softova, L. G.. - In: ST. PETERSBURG MATHEMATICAL JOURNAL. - ISSN 1061-0022. - STAMPA. - 31:3(2020), pp. 401-419. [10.1090/spmj/1605]
Survey on gradient estimates for nonlinear elliptic equations in various function spaces
Palagachev D. K.;
2020-01-01
Abstract
We study very general nonvariational elliptic equations of $p$-Laplacian type. We discuss an optimal Calder'on--Zygmund theory of 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 apply to Morrey spaces, Lorentz spaces and generalized Orlicz spaces as well.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
