Adapting some ideas from stochastic control theory to studying the heat equation in closed smooth domains

Nicolai V Krylov

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

Sufficient conditions on bounded domains D ⊂ ℝd = {(t,x)} of class C4 are given under which solutions of the heat equation ut = Δu + f in D have continuous second-order derivatives with respect to (t,x) in D̄. The equation is supplemented with C4 boundary data and it is assumed that f ∈ C2.

Original languageEnglish (US)
Pages (from-to)231-261
Number of pages31
JournalApplied Mathematics and Optimization
Volume46
Issue number2-3
DOIs
StatePublished - Sep 1 2002

Keywords

  • Conditional processes
  • Heat equation
  • Martingale inequalities

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