The $C^{\a}$ regularity of a class hypoelliptic ultraparabolic equations

Abstract

We obtained the $C^{\a}$ continuity for weak solutions of a class of ultraparabolic equations with measurable coefficients of the form ${\ptl_t u}= \sum_{i,j=1}^{m_0}X_i(a_{ij}(x,t)X_j u)+X_0 u$. The result is proved by simplifying and generalizing our earlier arguments for the $C^{\a}$ regularity of homogeneous ultraparabolic equations.

23 pages

References in corpus (1)

• The $C^{\a}$ regularity of a class hypoelliptic ultraparabolic equations

Cited by in corpus (14)

• The $C^{\a}$ regularity of a class hypoelliptic ultraparabolic equations
• The Landau equation with the specular reflection boundary condition
• Variational methods for the kinetic Fokker-Planck equation
• Velocity averaging and Hölder regularity for kinetic Fokker-Planck equations with general transport operators and rough coefficients
• Hölder continuity of solutions to hypoelliptic equations with bounded measurable coefficients
• A geometric statement of the Harnack inequality for a degenerate Kolmogorov equation with rough coefficients
• $C^{\alpha }$ regularity of weak solutions of non-homogenous ultraparabolic equations with drift terms
• A survey on the classical theory for Kolmogorov equation
• Global a priori estimates for the inhomogeneous Landau equation with moderately soft potentials
• Second order McKean-Vlasov SDEs and kinetic Fokker-Planck-Kolmogorov equations
• De Giorgi-Nash-Moser and H{ö}rmander theories: new interplay
• Quantitative spectral gaps and uniform lower bounds in the small noise limit for Markov semigroups generated by hypoelliptic stochastic differential equations
• The Hölder continuity of a class of 3-dimension ultraparabolic equations
• On a kinetic Poincaré inequality and beyond