\mathfrak{B}_{1} classes of De Giorgi, Ladyzhenskaya, and Ural'tseva and their application to elliptic and parabolic equations with nonstandard growth-Reference-Cited by-同舟云学术

\mathfrak{B}_{1} classes of De Giorgi, Ladyzhenskaya, and Ural'tseva and their application to elliptic and parabolic equations with nonstandard growth

Published:2019-10-21 Issue:3 Volume:16 Page:403-447
ISSN:1810-3200
Container-title:Ukrainian Mathematical Bulletin
language:uk
Short-container-title:UMB

Author:

Skrypnik Igor¹,Voitovych Mykhailo²

Affiliation:

1. Institute of Applied Mathematics and Mechanics of the NAS of Ukraine, Slavyansk, Ukraine; Vasyl' Stus Donetsk National University, Vinnytsia, Ukraine

2. Institute of Applied Mathematics and Mechanics of the NAS of Ukraine, Slavyansk, Ukraine

Abstract

The article provides an application of the generalized De Giorgi functional classes to the proof of the Hölder continuity of weak solutions to quasilinear elliptic and parabolic equations with nonstandard growth conditions.

Publisher

Institute of Applied Mathematics and Mechanics of the National Academy of Sciences of Ukraine

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