We study the discontinuous elliptic problem
where is a regular bounded domain of , is the Heaviside function, are a positive real parameters and h is a given function. We prove the existence of solutions, and characterize the free boundaries using the perturbation of the boundary condition and smooth boundary of the domain.
Submitted April 14, 2016. Published June 7, 2016.
Math Subject Classifications: 34R35, 35J25.
Key Words: Perturbation; implicit function theorem; free boundary problem.
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| Sabri Bensid |
Department of Mathematics
Faculty of Sciences
University of Tlemcen, B.P. 119
Tlemcen 13000, Algeria
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