A weighted L-p-theory for parabolic PDEs with BMO coefficients on C-1-domains

作者：Kim Kyeong Hun^*; Lee Kijung

来源：Journal of Differential Equations, 2013, 254(2): 368-407.

DOI：10.1016/j.jde.2012.08.002

• Parabolic equations
• Weighted Sobolev spaces
• L-p-theory
• BMO coefficients
• VMO coefficients

In this paper we present a weighted L-p-theory of second-order parabolic partial differential equations defined on C-1 domains. The leading coefficients are assumed to be measurable in time variable and have VMO (vanishing mean oscillation) or small BMO (bounded mean oscillation) with respect to space variables, and lower order coefficients are allowed to be unbounded and to blow up near the boundary. Our BMO condition is slightly relaxed than the others in the literature.

• 出版日期2013-1-15