Mixed local and nonlocal elliptic operators: regularity and maximum principles
Stefano Biagi, Serena Dipierro, Enrico Valdinoci, Eugenio Vecchi
2021Archivio istituzionale della ricerca (Alma Mater Studiorum Università di Bologna)135 citationsDOIOpen Access PDF
Abstract
We develop a systematic study of the superpositions of elliptic operators with different orders, mixing classical and fractional scenarios. For concreteness, we focus on the sum of the Laplacian and the fractional Laplacian, and we provide structural results, including existence, maximum principles (both for weak and classical solutions), interior Sobolev regularity and boundary regularity of Lipschitz type.
Topics & Concepts
MathematicsLipschitz continuitySobolev spaceLaplace operatorFractional LaplacianFocus (optics)Pure mathematicsMathematical analysisElliptic operatorMixing (physics)Type (biology)Boundary (topology)ConcretenessPhysicsOpticsBiologyPsychologyCognitive psychologyQuantum mechanicsEcologyNonlinear Partial Differential EquationsAdvanced Mathematical Modeling in EngineeringSpectral Theory in Mathematical Physics