Perturbation and Solvability of Initial Lp Dirichlet Problems for Parabolic Equations over Non-cylindrical Domains

Rivera-Noriega, Jorge

Canadian journal of mathematics, Tome 66 (2014) no. 2, pp. 429-452

Résumé

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.

Détail

DOI : 10.4153/CJM-2013-028-9

Mots-clés : 35K20, Initial Lp Dirichlet problem, second order parabolic equations in divergence form, noncylindrical domains, reverse Hölder inequalities

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