Abstract:In this paper, we consider the following free boundary problemThe domain Ω is a convex ring where Ω 1 and Ω 2 are bounded convex domain in R N , N ≥ 2, H is the Heaviside step function, λ, M, µ i (i = 1, .., n) are a given positive real parameters and φ is a given function . We show that under suitable conditions, there exists a solution to problem (P ) with a convex level set. We derive also an interesting result for the convexity of the set which is delimited by the free boundary in obstacle problem when the… Show more
Set email alert for when this publication receives citations?
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.