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Global \(C^{1,\alpha}\) regularity for variable exponent elliptic equations in divergence form.(English)Zbl 1143.35040

The author considers the elliptic equation in divergence form
\[-\text{div\,}A(x, u,Du)= B(x,u,Du)\quad\text{in }\Omega,\tag{1}\]
\[u= g\text{ on }\partial\Omega\text{ or }A(x,u,Du)\cdot\nu= h(x,u)\quad\text{on }\partial\Omega,\tag{2}\]
where \(\Omega\) is a bounded domain in \(\mathbb{R}^N\) and \(\nu\) is the outward unit normal to \(\partial\Omega\), \(A\) and \(B\) satisfy the variable exponent growth conditions. The goal of the author is to study the global \(C^{1,\alpha}\) regularity of the bounded generalized solutions to (1)–(2).

MSC:

35J60 Nonlinear elliptic equations
35J65 Nonlinear boundary value problems for linear elliptic equations
35D10 Regularity of generalized solutions of PDE (MSC2000)

Cite

References:

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[15]Ladyzenskaja, O. A.; Ural’tzeva, N. N., Linear and Quasilinear Elliptic Equations (1968), Academic Press: Academic Press New York ·Zbl 0164.13002
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This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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