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Real analytic solutions of parabolic equations with time-measurable coefficients


Author: Jay Kovats
Journal: Proc. Amer. Math. Soc. 130 (2002), 1055-1064
MSC (1991): Primary 35B65, 35K10
DOI: https://doi.org/10.1090/S0002-9939-01-06163-9
Published electronically: September 14, 2001
MathSciNet review: 1873779
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Abstract: We use Bernstein's technique to show that for any fixed $t$, strong solutions $u(t,x)$ of the uniformly parabolic equation $Lu:=a^{ij}(t)u_{x_{i}x_{j}}-u_{t}=0$ in $Q$ are real analytic in $Q(t)=\{x:(t,x)\in Q\}$. Here, $Q\subset \mathbb{R}^{d+1}$ is a bounded domain and the coefficients $a^{ij}(t)$ are measurable. We also use Bernstein's technique to obtain interior estimates for pure second derivatives of solutions of the fully nonlinear, uniformly parabolic, concave equation $F(D^{2}u,t)-u_{t}=0$ in $Q$, where $F$ is measurable in $t$.


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Additional Information

Jay Kovats
Affiliation: Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, Florida 32901
Email: jkovats@zach.fit.edu

DOI: https://doi.org/10.1090/S0002-9939-01-06163-9
Received by editor(s): October 4, 2000
Published electronically: September 14, 2001
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2001 American Mathematical Society

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