Small perturbation solutions for parabolic equations
Yu Wang
35J6035B65Perturbation theoryViscosity solutions.
Let $\varphi$ be a smooth solution of the parabolic equation
\[
F(D^2u,Du,u,x,t)-u_t=0.
\]
Assume that $F$ is smooth and uniformly elliptic only in a neighborhood of the points $(\DD^2\varphi,D\varphi,\varphi,x,t)$. Then, we show that a viscosity solution $u$ to the above equation is smooth in the interior if $\|u-\varphi\|_{L^{\infty}}$ is sufficiently small.
Indiana University Mathematics Journal
2013
text
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10.1512/iumj.2013.62.4961
10.1512/iumj.2013.62.4961
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Indiana Univ. Math. J. 62 (2013) 671 - 697
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