Abstract
In this paper we study questions of existence, uniqueness, and continuous dependence for semilinear elliptic equations with nonlinear boundary conditions. In particular, we obtain results concerning the continuous dependence of the solutions on the nonlinearities in the problem, which in turn implies analogous results for a related parabolic problem. Such questions arise naturally in the study of potential theory, flow through porous media, and obstacle problems.
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Communicated by D. Kinderlehrer
Sponsored by the United States Army under Contract Nos. DAAG29-80-C-0041 and DAAL03-87-K-0043, and by the Air Force Office of Scientific Research under Contract No. AFOSR 84-0252 and by the National Science Foundation under Grant No. DMS-8505531. Research of the third author was carried out in part while visiting the Institute for Mathematics and Its Applications at the University of Minnesota.
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Benilan, P., Crandall, M.G. & Sacks, P. SomeL 1 existence and dependence results for semilinear elliptic equations under nonlinear boundary conditions. Appl Math Optim 17, 203–224 (1988). https://doi.org/10.1007/BF01448367
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DOI: https://doi.org/10.1007/BF01448367