A-priori bound and Hölder continuity of solutions to degenerate elliptic equations with variable exponents
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Published:2022-12-10
Issue:
Volume:
Page:1-32
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ISSN:1230-3429
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Container-title:Topological Methods in Nonlinear Analysis
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language:
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Short-container-title:TMNA
Author:
Ho KyORCID,
Nhan Le CongORCID,
Truong Le XuanORCID
Abstract
We investigate the boundedness and regularity of solutions to degenerate elliptic equations with variable exponents that are subject to the Dirichlet boundary condition.
By employing the De Giorgi iteration, we obtain a-priori bounds and the Hölder continuity for solutions.
As an application, we obtain the existence of infinitely many small solutions for a class of degenerate elliptic equations involving variable exponents.
Publisher
Uniwersytet Mikolaja Kopernika/Nicolaus Copernicus University
Subject
Applied Mathematics,Analysis