$C^{\alpha }$ regularity of weak solutions of non-homogenous ultraparabolic equations with drift terms

Abstract

Consider a class of non-homogenous ultraparabolic differential equations with drift terms or lower order terms arising from some physical models, and we prove that weak solutions are Hölder continuous, which also generalizes the classic results of parabolic equations of second order. The main ingredients are a type of weak Poincaré inequality satisfied by non-negative weak sub-solutions and Moser iteration.

We delete the Prandtl part and add some details for $L^{\infty }$ estimate. arXiv admin note: text overlap with arXiv:0711.3411

References in corpus (1)

• Hölder continuity of solutions to hypoelliptic equations with bounded measurable coefficients

Cited by in corpus (1)

• Moser's estimates for degenerate Kolmogorov equations with non-negative divergence lower order coefficients