Quantitative De Giorgi methods in kinetic theory
Jessica Guerand, Clément Mouhot
Abstract
We consider hypoelliptic equations of kinetic Fokker-Planck type, also known as Kolmogorov or ultraparabolic equations, with rough coefficients in the drift-diffusion operator. We give novel short quantitative proofs of the De Giorgi intermediate-value Lemma as well as weak Harnack and Harnack inequalities. This implies Hölder continuity with quantitative estimates. The paper is self-contained.
Topics & Concepts
Lemma (botany)MathematicsHypoelliptic operatorMathematical proofHarnack's inequalityOperator (biology)Pure mathematicsDiffusionType (biology)Kinetic energyApplied mathematicsMathematical analysisPhysicsThermodynamicsGeometryQuantum mechanicsGeneBiochemistryRepressorBiologyChemistrySemi-elliptic operatorEcologyTranscription factorPoaceaeDifferential operatorGas Dynamics and Kinetic TheoryNumerical methods in inverse problemsMathematical Biology Tumor Growth