On a Steklov-Robin eigenvalue problem

In this paper we study a Steklov-Robin eigenvalue problem for the Laplacian in annular domains. More precisely, we consider Omega = Omega(0) \ (B) over bar (r), where B-r is the ball centered at the origin with radius r > 0 and Omega(0) subset of R-n, n >= 2, is an open, bounded set with Lipschitz boundary, such that (B) over bar (r) subset of Omega(0). We impose a Steklov condition on the outer boundary and a Robin condition involving a positive L-infinity function beta(x) on the inner boundary. Then, we study the first eigenvalue sigma(beta)(Omega) and its main properties. In particular, we investigate the behavior of sigma(beta)(Omega) when we let vary the L-1-norm of beta and the radius of the inner ball. Furthermore, we study the asymptotic behavior of the corresponding eigenfunctions when beta is a positive parameter that goes to infinity. (c) 2023 Elsevier Inc. All rights reserved.

Automated summary

In this paper, we investigate the Steklov-Robin eigenvalue problem for the Laplacian in annular domains. We consider a specific type of annular domain and impose Steklov and Robin conditions on the boundaries. We study the first eigenvalue and its properties, including the behavior when varying the norm of beta and the radius of the inner ball. We also analyze the asymptotic behavior of the corresponding eigenfunctions as beta approaches infinity.