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1. CJM 2013 (vol 66 pp. 429)

Rivera-Noriega, Jorge
 Perturbation and Solvability of Initial $L^p$ Dirichlet Problems for Parabolic Equations over Non-cylindrical Domains 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 $1\lt p\lt \infty$ 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 $p\gt 1$, the initial $L^p$ Dirichlet problem associated to $Lu=0$ over non-cylindrical domains is solvable. The results are adequate adaptations of the corresponding results for elliptic equations. Keywords:initial $L^p$ Dirichlet problem, second order parabolic equations in divergence form, non-cylindrical domains, reverse HÃ¶lder inequalitiesCategory:35K20

2. CJM 1997 (vol 49 pp. 798)

Yu, Minqi; Lian, Xiting
 Boundedness of solutions of parabolic equations with anisotropic growth conditions In this paper, we consider the parabolic equation with anisotropic growth conditions, and obtain some criteria on boundedness of solutions, which generalize the corresponding results for the isotropic case. Keywords:Parabolic equation, anisotropic growth conditions, generalized, solution, boundnessCategories:35K57, 35K99.
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