A-priori bound and Hölder continuity of solutions to degenerate elliptic equations with variable exponents
DOI:
https://doi.org/10.12775/TMNA.2022.021Keywords
p(.)-Laplacian, weighted variable exponent Lebesgue-Sobolev spaces, a-priori bound, Hölder continuity, De Giorgi iteration, localization methodAbstract
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.References
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