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Gradient estimates for semilinear elliptic equations

Published online by Cambridge University Press:  14 November 2011

Gary M. Lieberman
Gary M. Lieberman
Affiliation:
Department of Mathematics, Iowa State University, Ames, Iowa 50011, U.S.A.and Centre for Mathematical Analysis, Australian National University, G.P.O. Box 4, Canberra, A.C.T. 2601, Australia
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Synopsis

Estimates on the gradient of solutions to the Dirichlet problem for a semilinear elliptic equation are given when the nonlinearity in the equation is quadratic with respect to the gradient of the solution. These estimates extend results of F. Tomi to less smooth boundary data and results of the author to the full quadratic growth.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 100 , Issue 1-2 , 1985 , pp. 11 - 17
Copyright
Copyright © Royal Society of Edinburgh 1985

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References

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