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

Paul M.N. Feehan, Camelia A. Pop

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14 Scopus citations

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 C-smooth source function, we prove C-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 [10,25], generators of diffusion processes arising in mathematical biology [3,11], and the study of porous media [7,8].

Original languageEnglish (US)
Pages (from-to)895-956
Number of pages62
JournalJournal of Differential Equations
Volume256
Issue number3
DOIs
StatePublished - Feb 1 2014

Keywords

  • A priori Schauder estimate
  • Boundary-degenerate elliptic partial differential operator
  • Degenerate diffusion process
  • Hölder regularity
  • Mathematical finance
  • Primary
  • Secondary

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