Asymptotic behaviour of fundamental solutions and potential theory of parabolic operators with variable coefficients

DOI10.1007/BF01446432zbMath0638.35003OpenAlexW2075970446MaRDI QIDQ1099326

Nicola Garofalo, Ermanno Lanconelli

Publication date: 1989

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/164505

zbMATH Keywords

regularityDirichlet problemHarnack inequalityasymptotic expansionfundamental solutionnonnegative solutionsharmonic functionsvariable coefficientsmean value formulasparabolic potential theoryregularity of boundary pointsL-superparabolic functions

Mathematics Subject Classification ID

Fundamental solutions to PDEs (35A08) Asymptotic expansions of solutions to PDEs (35C20) Harmonic, subharmonic, superharmonic functions on other spaces (31C05) Second-order parabolic equations (35K10)

Related Items (16)

Some properties of sub-Laplaceans ⋮ Harnack inequality and Liouville-type theorems for Ornstein-Uhlenbeck and Kolmogorov operators ⋮ The strong maximum principle and the Harnack inequality for a class of hypoelliptic non-Hörmander operators ⋮ Mean value formulas for classical solutions to uniformly parabolic equations in the divergence form with non‐smooth coefficients ⋮ Subharmonic functions in sub-Riemannian settings ⋮ Blaschke, Privaloff, Reade and Saks theorems for diffusion equations on Lie groups ⋮ Local monotonicity and mean value formulas for evolving Riemannian manifolds ⋮ Trace heat kernel asymptotics in 3D contact sub-Riemannian geometry ⋮ Wiener's criterion for divergence form parabolic operators with \(C^ 1\)- Dini continuous coefficients ⋮ On Mean Value formulas for solutions to second order linear PDEs ⋮ Some estimates of fundamental solutions on noncompact manifolds with time-dependent metrics ⋮ The Role of Fundamental Solution in Potential and Regularity Theory for Subelliptic PDE ⋮ Dynamics of Dislocation Densities in a Bounded Channel. Part II: Existence of Weak Solutions to a Singular Hamilton–Jacobi/Parabolic Strongly Coupled System ⋮ Level Sets of the Fundamental Solution and Harnack Inequality for Degenerate Equations of Kolmogorov Type ⋮ The theory of energy for sub-Laplacians with an application to quasi-continuity ⋮ Sobolev-type inequalities and heat kernel bounds along the geometric flow

Cites Work

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• Mean value properties of solutions to parabolic equations with variable coefficients
• Wiener's criterion for the heat equation
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• Maggioranti e minoranti delle soluzioni delle equazioni paraboliche
• Sulla soluzione generalizzata di Wiener per il primo problema di valori al contorno nel caso parabolico
• Wiener's Criterion for Parabolic Equations with Variable Coefficients and Its Consequences
• Off diagonal short time asymptotics for fundamental solution of diffusion equation
• A harnack inequality for parabolic differential equations
• A Mean Value Theorem for the Heat Equation
• A Theory of Subtemperatures in Several Variables

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