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Adapting Some Ideas from Stochastic Control Theory to Studying the Heat Equation in Closed Smooth Domains

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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 u t =Δ u+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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  1. 127 Vincent Hall, University of Minnesota, Minneapolis, MN, 55455, USA krylov@math.umn.edu, , , , , , US

    Nicolai V. Krylov

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  1. Nicolai V. Krylov
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Nicolai V. Krylov, . Adapting Some Ideas from Stochastic Control Theory to Studying the Heat Equation in Closed Smooth Domains . Appl Math Optim 46, 231–261 (2002). https://doi.org/10.1007/s00245-002-0745-3

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  • DOI: https://doi.org/10.1007/s00245-002-0745-3

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