Boundedness and Hölder continuity of weak solutions of the nonlinear boundary-value problem for elliptic equations with general nonstandard growth conditions

Boundedness and Hölder continuity of weak solutions of the nonlinear boundary-value problem for elliptic equations with general nonstandard growth conditions

We study a nonlinear boundary-value problem for elliptic equations with critical growth conditions involving Lebesgue measurable functions. We prove global boundedness and Hölder continuity of weak solutions for this problem. Our results generalize the ones obtained by P. Winkert and his colleagues...

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Bibliographic Details
Main Authors: Gumpyong Ri, Dukman Ri
Format: Article
Language:English
Published: Institute of Mathematics of the Czech Academy of Science 2025-07-01
Series:Mathematica Bohemica
Subjects:
nonstandard growth
nonlinear boundary condition
hölder continuity
boundedness
Online Access:https://mb.math.cas.cz/full/150/2/mb150_2_1.pdf
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Summary:We study a nonlinear boundary-value problem for elliptic equations with critical growth conditions involving Lebesgue measurable functions. We prove global boundedness and Hölder continuity of weak solutions for this problem. Our results generalize the ones obtained by P. Winkert and his colleagues (2012) not only in the variable exponent case but also in the constant exponent case.
ISSN:0862-7959
2464-7136

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