Boundary Estimates for a Degenerate Parabolic Equation with Partial Dirichlet Boundary Conditions

Charles L. Epstein, Camelia A. Pop

Research output: Contribution to journalArticlepeer-review


We study the boundary regularity properties and derive pointwise a priori supremum estimates of weak solutions and their derivatives in terms of suitable weighted L2-norms for a class of degenerate parabolic equations that satisfy homogeneous Dirichlet boundary conditions on certain portions of the boundary. Such equations arise in population genetics in the study of models for the evolution of gene frequencies. Among the applications of our results is the description of the structure of the transition probabilities and of the hitting distributions of the underlying gene frequencies process.

Original languageEnglish (US)
Pages (from-to)2377-2421
Number of pages45
JournalJournal of Geometric Analysis
Issue number3
StatePublished - Jul 1 2020
Externally publishedYes

Bibliographical note

Funding Information:
CLE research partially supported by the NSF under Grant DMS-1507396, and by the ARO under Grant W911NF-12-1-0552. CP gratefully acknowledges the support and hospitality provided by the IMA during the academic year 2015–2016.

Publisher Copyright:
© 2017, Mathematica Josephina, Inc.


  • A priori Sobolev estimates
  • A priori supremum estimates
  • Boundary regularity
  • Degenerate elliptic operators


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