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Search: MSC category 35B65 ( Smoothness and regularity of solutions )

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1. CJM 2009 (vol 62 pp. 202)

Tang, Lin
Interior $h^1$ Estimates for Parabolic Equations with $\operatorname{LMO}$ Coefficients
In this paper we establish \emph{a priori} $h^1$-estimates in a bounded domain for parabolic equations with vanishing $\operatorname{LMO}$ coefficients.

Keywords:parabolic operator, Hardy space, parabolic, singular integrals and commutators
Categories:35K20, 35B65, 35R05

2. CJM 2007 (vol 59 pp. 1301)

Furioli, Giulia; Melzi, Camillo; Veneruso, Alessandro
Strichartz Inequalities for the Wave Equation with the Full Laplacian on the Heisenberg Group
We prove dispersive and Strichartz inequalities for the solution of the wave equation related to the full Laplacian on the Heisenberg group, by means of Besov spaces defined by a Littlewood--Paley decomposition related to the spectral resolution of the full Laplacian. This requires a careful analysis due also to the non-homogeneous nature of the full Laplacian. This result has to be compared to a previous one by Bahouri, G\'erard and Xu concerning the solution of the wave equation related to the Kohn Laplacian.

Keywords:nilpotent and solvable Lie groups, smoothness and regularity of solutions of PDEs
Categories:22E25, 35B65

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