Absence of eigenvalues of non‐self‐adjoint Robin Laplacians on the half‐space
L. Cossetti, D. Krejčiřík
Abstract
By developing the method of multipliers, we establish sufficient conditions which guarantee the total absence of eigenvalues of the Laplacian in the half-space, subject to variable complex Robin boundary conditions. As a further application of this technique, uniform resolvent estimates are derived under the same assumptions on the potential. Some of the results are new even in the self-adjoint setting, where we obtain quantum-mechanically natural conditions.
Topics & Concepts
MathematicsResolventEigenvalues and eigenvectorsLaplace operatorBoundary (topology)Pure mathematicsVariable (mathematics)Mathematical analysisMathematics Subject ClassificationRobin boundary conditionBoundary value problemApplied mathematicsp-LaplacianSpectral Theory in Mathematical PhysicsNonlinear Partial Differential EquationsStability and Controllability of Differential Equations