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

Nicolai V. Krylov

doi:10.1007/s00245-002-0745-3

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

Nicolai V. Krylov

Mathematics

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7 Scopus citations

Abstract

Sufficient conditions on bounded domains D ⊂ ℝ^d = {(t,x)} of class C⁴ are given under which solutions of the heat equation u_t = 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 language	English (US)
Pages (from-to)	231-261
Number of pages	31
Journal	Applied Mathematics and Optimization
Volume	46
Issue number	2-3
DOIs	https://doi.org/10.1007/s00245-002-0745-3
State	Published - Sep 2002

Keywords

Conditional processes
Heat equation
Martingale inequalities

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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 {\=D}. The equation is supplemented with C4 boundary data and it is assumed that f ∈ C2.",

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AB - 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.

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KW - Heat equation

KW - Martingale inequalities

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

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