Existence and symmetry for elliptic equations in a,, super(n) with arbitrary growth in the gradient
We study the semilinear elliptic equation Delta u + g(x, u, Du) = 0 in a,, super(n). The nonlinearities g can have arbitrary growth in u and Du, including, in particular, exponential behavior. No restriction is imposed on the behavior of g(x, z, p) at infinity except in the variable x. We obtain a s...
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Published in | Journal d'analyse mathématique (Jerusalem) Vol. 130; no. 1; pp. 1 - 18 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
01.11.2016
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Subjects | |
Online Access | Get full text |
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Summary: | We study the semilinear elliptic equation Delta u + g(x, u, Du) = 0 in a,, super(n). The nonlinearities g can have arbitrary growth in u and Du, including, in particular, exponential behavior. No restriction is imposed on the behavior of g(x, z, p) at infinity except in the variable x. We obtain a solution u which is locally unique and inherits many of the symmetry properties of g. Positivity and asymptotic behavior of the solution are also addressed. Our results can be extended to other domains, such as the half-space and exterior domains. Finally, we give some examples. |
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Bibliography: | ObjectType-Article-1 SourceType-Scholarly Journals-1 content type line 23 ObjectType-Feature-2 |
ISSN: | 0021-7670 1565-8538 |
DOI: | 10.1007/s11854-016-0027-7 |