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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On the existence and boundary behavior of solutions to a class of nonlinear Dirichlet problems


Authors: Carlos E. Kenig and Wei-Ming Ni
Journal: Proc. Amer. Math. Soc. 89 (1983), 254-258
MSC: Primary 35J65; Secondary 35J67
MathSciNet review: 712633
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Abstract: In this paper, we first extend the well-known method of super- and sub-solutions for elliptic boundary value problems to $ {L^\infty }$-boundary functions. Then we apply this method to investigate the solvability and the boundary behavior of solutions to some nonlinear elliptic equations, some Fatou-type results are obtained.


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DOI: https://doi.org/10.1090/S0002-9939-1983-0712633-3
Article copyright: © Copyright 1983 American Mathematical Society