Interior \(W^{1,p}\) regularity and Hölder continuity of weak solutions to a class of divergence Kolmogorov equations with discontinuous coefficients

DOI10.1007/s00032-013-0203-5zbMath1364.35153OpenAlexW2083546078MaRDI QIDQ383904

Maochun Zhu, Peng Cheng Niu

Publication date: 6 December 2013

Published in: Milan Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00032-013-0203-5

zbMATH Keywords

regularitysingular integraldivergence Kolmogorov equationlocally homogeneous spaces

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Reaction-diffusion equations (35K57) Degenerate parabolic equations (35K65) Ultraparabolic equations, pseudoparabolic equations, etc. (35K70)

Related Items

Global existence and asymptotic behavior of solutions to a semilinear parabolic equation on Carnot groups ⋮ Interior \(W_\ast^{1, p(x, t)}\)-regularity for parabolic divergence equations of Hörmander's type ⋮ Interior regularity for degenerate equations with drift on homogeneous groups

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Local real analysis in locally homogeneous spaces
• Global \(L^{p}\) estimates for degenerate Ornstein-Uhlenbeck operators
• Schauder estimates for parabolic nondivergence operators of Hörmander type
• Schauder estimates, Harnack inequality and Gaussian lower bound for Kolmogorov-type operators in non-divergence form
• Singular integrals in nonhomogeneous spaces: \(L^2\) and \(L^p\) continuity from Hölder estimates
• Subelliptic estimates and function spaces on nilpotent Lie groups
• \(\mathcal{L}^p\) estimates for some ultraparabolic operators with discontinuous coefficients
• Hypoelliptic second order differential equations
• Analyse harmonique non-commutative sur certains espaces homogènes. Etude de certaines intégrales singulières. (Non-commutative harmonic analysis on certain homogeneous spaces. Study of certain singular integrals.)
• On Boltzmann and Landau equations
• 𝐿^{𝑝} estimates for nonvariational hypoelliptic operators with 𝑉𝑀𝑂 coefficients
• Hölder regularity for solutions of ultraparabolic equations in divergence form