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

Kenig, Carlos E.; Ni, Wei-Ming

doi:10.1090/S0002-9939-1983-0712633-3

On the existence and boundary behavior of solutions to a class of nonlinear Dirichlet problems
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by Carlos E. Kenig and Wei-Ming Ni PDF

Proc. Amer. Math. Soc. 89 (1983), 254-258 Request permission

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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