Existence and comparison results for quasilinear elliptic equations with critical growth in the gradient (Q5933459)
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scientific article; zbMATH DE number 1599078
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Existence and comparison results for quasilinear elliptic equations with critical growth in the gradient |
scientific article; zbMATH DE number 1599078 |
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Existence and comparison results for quasilinear elliptic equations with critical growth in the gradient (English)
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14 November 2001
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semilinear problem
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existence of solutions
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symmetrized problems
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It is given a condition of existence of bounded solutions for a general quasilinear elliptic problem NEWLINE\[NEWLINE -\text{ div } A(x,u,Du)=H(x,u,Du)\quad \text{ in} \Omega,\quad u\in W^{1,p}_0(\Omega)\cap L^\infty(\Omega) NEWLINE\]NEWLINE supposing quadratic growth in the gradient and small enough data. It is obtained an a.e. comparison with the semilinear symmetrized problem.
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