Generalized nonlocal Robin Laplacian on arbitrary domains

Robin Boundary Value Problems on Arbitrary Domains

We develop a theory of generalised solutions for elliptic boundary value problems subject to Robin boundary conditions on arbitrary domains, which resembles in many ways that of the Dirichlet problem. In particular, we establish Lp-Lq-estimates which turn out to be the best possible in that framework. We also discuss consequences to the spectrum of Robin boundary value problems. Finally, we app...

Tunneling for the Robin Laplacian in smooth planar domains

We study the low-lying eigenvalues of the semiclassical Robin Laplacian in a smooth planar domain with bounded boundary which is symmetric with respect to an axis. In the case when the curvature of the boundary of the domain attains its maximum at exactly two points away from the axis of symmetry, we establish an explicit asymptotic formula for the splitting of the first two eigenvalues. This i...

Generalized Robin Boundary Conditions, Robin-to-dirichlet Maps, and Krein-type Resolvent Formulas for Schrödinger Operators on Bounded Lipschitz Domains

We study generalized Robin boundary conditions, Robin-to-Dirichlet maps, and Kreintype resolvent formulas for Schrödinger operators on bounded Lipschitz domains in R, n > 2. We also discuss the case of bounded C-domains, (1/2) < r < 1.

On the Nonhomogeneous Fourth-Order p-Laplacian Generalized Sturm-Liouville Nonlocal Boundary Value Problems

On the Robin Problem in Fractal Domains

We study the solution to the Robin boundary problem for the Laplacian in a Euclidean domain. We present some families of fractal domains where the infimum is greater than 0, and some other families of domains were it is equal to 0. We also give a new result on “trap domains” defined in [BCM], i.e., domains where reflecting Brownian motion takes a long time to reach the center of the domain.