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Perturbation and Solvability of Initial Lp Dirichlet Problems for Parabolic Equations over Non-cylindrical Domains
Published online by Cambridge University Press: 20 November 2018
Abstract
For parabolic linear operators $L$ of second order in divergence form, we prove that the solvability of initial
${{L}^{p}}$ Dirichlet problems for the whole range
$1\,<\,p\,<\,\infty $ is preserved under appropriate small perturbations of the coefficients of the operators involved. We also prove that if the coefficients of
$L$ satisfy a suitable controlled oscillation in the form of Carleson measure conditions, then for certain values of
$p\,>\,1$, the initial
${{L}^{p}}$ Dirichlet problem associated with
$Lu\,=\,0$ over non-cylindrical domains is solvable. The results are adequate adaptations of the corresponding results for elliptic equations.
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- Copyright © Canadian Mathematical Society 2014
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