$C^{1,\alpha }$ regularity for elliptic equations with the general nonstandard growth conditions

Kim, Sungchol ; Ri, Dukman

Mathematica Bohemica, Tome 149 (2024) no. 3, pp. 365-396

Abstract (VO)

We study elliptic equations with the general nonstandard growth conditions involving Lebesgue measurable functions on $\Omega $. We prove the global $C^{1, \alpha }$ regularity of bounded weak solutions of these equations with the Dirichlet boundary condition. Our results generalize the $C^{1, \alpha }$ regularity results for the elliptic equations in divergence form not only in the variable exponent case but also in the constant exponent case.

Détail

DOI : 10.21136/MB.2023.0055-23

Classification : 35B65, 35D30, 35J25
Keywords: nonstandard growth; $C^{1, \alpha }$ regularity; Hölder continuity; bounded weak solution; partial differential equations

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