A Faber-Krahn inequality for mixed local and nonlocal operators
Stefano Biagi, Serena Dipierro, Enrico Valdinoci, Eugenio Vecchi
Abstract
Abstract We consider the first Dirichlet eigenvalue problem for a mixed local/nonlocal elliptic operator and we establish a quantitative Faber-Krahn inequality. More precisely, we show that balls minimize the first eigenvalue among sets of given volume and we provide a stability result for sets that almost attain the minimum.
Topics & Concepts
Eigenvalues and eigenvectorsMathematicsOperator (biology)InequalityDirichlet distributionStability (learning theory)Dirichlet eigenvalueApplied mathematicsPure mathematicsMathematical analysisComputer sciencePhysicsDirichlet's principleChemistryQuantum mechanicsBiochemistryRepressorGeneTranscription factorMachine learningBoundary value problemNonlinear Partial Differential EquationsAdvanced Mathematical Modeling in EngineeringNumerical methods in inverse problems