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

Abstract

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. 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.

58 pages, 1 figure. To appear in the Journal of Differential Equations. Incorporates final galley proof corrections corresponding to published version

References in corpus (4)

• A Schauder approach to degenerate-parabolic partial differential equations with unbounded coefficients
• Existence, uniqueness, and global regularity for degenerate elliptic obstacle problems in mathematical finance
• Maximum principles for boundary-degenerate second-order linear elliptic differential operators
• Degenerate-elliptic operators in mathematical finance and higher-order regularity for solutions to variational equations

Cited by in corpus (11)

• A Schauder approach to degenerate-parabolic partial differential equations with unbounded coefficients
• C^{1,1} regularity for degenerate elliptic obstacle problems
• Singular parabolic equations of second order on manifolds with singularities
• Stochastic representation of solutions to degenerate elliptic and parabolic boundary value and obstacle problems with Dirichlet boundary conditions
• Degenerate-elliptic operators in mathematical finance and higher-order regularity for solutions to variational equations
• Parabolic and elliptic equations with singular or degenerate coefficients: the Dirichlet problem
• Boundary estimates for a degenerate parabolic equation with partial Dirichlet boundary conditions
• Sharp two-sided Green function estimates for Dirichlet forms degenerate at the boundary
• Dirichlet boundary conditions for degenerate and singular nonlinear parabolic equations
• Dimensional Universality of Schauder Estimates Constants for Fourth Order Heat-Type Equations
• Weighted $W^{1,p}$- estimates for weak solutions of degenerate elliptic equations with coefficients degenerate in one variable