A counterexample to Schauder estimates for elliptic operators with unbounded coefficients

Enrico Priola

Displaying similar documents to “A counterexample to Schauder estimates for elliptic operators with unbounded coefficients”

Global Schauder estimates for a class of degenerate Kolmogorov equations

Enrico Priola (2009)

Studia Mathematica

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We consider a class of possibly degenerate second order elliptic operators on ℝⁿ. This class includes hypoelliptic Ornstein-Uhlenbeck type operators having an additional first order term with unbounded coefficients. We establish global Schauder estimates in Hölder spaces both for elliptic equations and for parabolic Cauchy problems involving . The Hölder spaces in question are defined with respect to a possibly non-Euclidean metric related to the operator . Schauder estimates are deduced...

The parabolic mixed Cauchy-Dirichlet problem in spaces of functions which are hölder continuous with respect to space variables

Davide Guidetti (1996)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We give a new proof, based on analytic semigroup methods, of a maximal regularity result concerning the classical Cauchy-Dirichlet's boundary value problem for second order parabolic equations. More specifically, we find necessary and sufficient conditions on the data in order to have a strict solution $u$ which is bounded with values in $C^{2 + θ} (\bar{Ω})$ (0 < < 1), with $\partial_{t} u$ bounded with values in $C^{θ} (\bar{Ω})$ .

On the regularity of solutions of a thermoelastic system under noncontinuous heating regimes. II

Jiří Jarušek (1991)

Applications of Mathematics

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A quasilinear noncoupled thermoelastic system is studied both on a threedimensional bounded domain with a smooth boundary and for a generalized model involving the influence of supports. Sufficient conditions are derived under which the stresses are bounded and continuous on the closure of the domain.

Nonunique continuation for plane uniformly elliptic equations in Sobolev spaces

Pasquale Buonocore, Paolo Manselli (2000)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Carleman estimates for a subelliptic operator and unique continuation

Nicola Garofalo, Zhongwei Shen (1994)

Annales de l'institut Fourier

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We establish a Carleman type inequality for the subelliptic operator $ℒ = Δ_{z} + | x |^{2} \partial_{t}^{2}$ in $ℝ^{n + 1}$ , $n \geq 2$ , where $z \in ℝ^{n}$ , $t \in ℝ$ . As a consequence, we show that $- ℒ + V$ has the strong unique continuation property at points of the degeneracy manifold ${(0, t) \in ℝ^{n + 1} | t \in ℝ}$ if the potential $V$ is locally in certain $L^{p}$ spaces.