Improvement of Flatness for Nonlocal Phase Transitions
Serena Dipierro, Joaquim Serra, Enrico Valdinoci
Abstract
We prove an improvement of flatness result for nonlocal phase transitions. For a class of nonlocal equations, we obtain a result in the same spirit of a celebrated theorem of Savin for the classical case. The results presented are completely new even for the case of the fractional Laplacian, but the robustness of the proofs allows us to treat also more general, possibly anisotropic, integro-differential operators.
Topics & Concepts
Flatness (cosmology)MathematicsFractional LaplacianMathematical proofLaplace operatorRobustness (evolution)Phase transitionAnisotropyPure mathematicsMathematical physicsMathematical analysisPhysicsQuantum mechanicsGeometryCosmologyChemistryBiochemistryGeneNonlinear Partial Differential EquationsAdvanced Mathematical Modeling in EngineeringNumerical methods in inverse problems