Maria A. Shan, Igor I. Skrypnik, Mykhailo V. Voitovych
Abstract:
We prove Harnack's inequality for bounded weak solutions to quasilinear second order
elliptic equations with generalized Orlicz growth conditions.
Our approach covers new cases of variable exponent and (p,q) growth conditions.
Submitted September 7, 2020. Published April 7, 2021.
Math Subject Classifications: 35B65, 35D30, 35J60, 49N60.
Key Words: Elliptic equation; non-standard growth; non-log condition;
bounded solution; Harnack inequality.
DOI: https://doi.org/10.58997/ejde.2021.27
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Maria A. Shan Institute of Applied Mathematics and Mechanics National Academy of Sciences of Ukraine Gen. Batiouk str. 19, 84116 Sloviansk, Ukraine email: shan_maria@ukr.net |
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Igor I. Skrypnik Institute of Applied Mathematics and Mechanics National Academy of Sciences of Ukraine Gen. Batiouk str. 19, 84116 Sloviansk, Ukraine email: iskrypnik@iamm.donbass.com |
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Mykhailo V. Voitovych Institute of Applied Mathematics and Mechanics National Academy of Sciences of Ukraine Gen. Batiouk str. 19, 84116 Sloviansk, Ukraine email: voitovichmv76@gmail.com |
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