On the interior \(C^{2,\alpha}\) regularity of solutions of nonlinear elliptic equations (Q2780420)
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scientific article; zbMATH DE number 1728946
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the interior \(C^{2,\alpha}\) regularity of solutions of nonlinear elliptic equations |
scientific article; zbMATH DE number 1728946 |
Statements
13 July 2003
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fractional derivative
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\(L^p\) estimates technique
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On the interior \(C^{2,\alpha}\) regularity of solutions of nonlinear elliptic equations (English)
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The author deals with the interior \(C^{2,\alpha}\) regularity of classical solutions \(u\in C^2(\Omega)\) of nonlinear uniformly elliptic equations NEWLINE\[NEWLINEF\bigl(x,u(x), Du(x),D^2u(x) \bigr)=0.NEWLINE\]NEWLINE Under some suitable assumptions on \(F\) and its derivatives it is shown that \(u\in C^{2,\alpha} (\Omega)\). To this end the author uses fractional derivative, \(L^p\) estimates techniques.
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