Schauder a priori estimates and regularity of solutions to boundary-degenerate elliptic linear second-order partial differential equations

详细信息    查看全文

• 作者：Paul M.N. Feehan ; Camelia A. Pop
• 关键词：primary ; 35J70 ; secondary ; 60J60
• 刊名：Journal of Differential Equations
• 出版年：1 February, 2014
• 年：2014
• 卷：256
• 期：3
• 页码：895-956
• 全文大小：942 K

文摘

We establish Schauder a priori estimates and regularity for solutions to a class of boundary-degenerate elliptic linear second-order partial differential equations. Furthermore, given a -smooth source function, we prove -regularity of solutions up to the portion of the boundary where the operator is degenerate. Boundary-degenerate elliptic operators of the kind described in our article appear in a diverse range of applications, including as generators of affine diffusion processes employed in stochastic volatility models in mathematical finance , generators of diffusion processes arising in mathematical biology , and the study of porous media .