Geodesic
$C^{1,\alpha }$ regularity for elliptic equations with the general nonstandard growth conditions
Mathematica Bohemica, Tome 149 (2024) no. 3, pp. 365-396 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
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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Kim, Sungchol; Ri, Dukman. $C^{1,\alpha }$ regularity for elliptic equations with the general nonstandard growth conditions. Mathematica Bohemica, Tome 149 (2024) no. 3, pp. 365-396. doi: 10.21136/MB.2023.0055-23

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