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$L^{p}$ -approximation of generalized biaxially symmetric potentials over Carathéodory domains

Harvir S. Kasana, Devendra Kumar (2005)

Mathematica Slovaca

La conjecture de Kato

Yves Meyer (2001/2002)

Séminaire Bourbaki

L'equazione $\Delta_{2}u+a_{10}(x,y)\frac{\partial u}{\partial x}+a_{01}(x,y)\frac{\partial u% }{\partial y}+a_{00}(x,y)u=F(x,y)$ . Teoremi di completezza

Alberto Cialdea (1987)

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

In ipotesi molto generali si dimostrano teoremi di completezza nel senso di Picone per l'equazione (1). Come corollario si ottengono teoremi del tipo Runge.

L'equazione $\Delta_{2}u+a_{10}(x,y)\frac{\partial u}{\partial x}+a_{01}(x,y)\frac{\partial u% }{\partial y}+a_{00}(x,y)u=F(x,y)$ . Calcolo dell'indice dei problemi al contorno e soluzioni deboli

Alberto Cialdea (1986)

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

It is proved that Lopatinskii's condition is necessary and sufficient for problem (2.5) to be an index problem. A method is given for the determination of the index.

Limit behaviour of singular solutions of some semilinear elliptic equations

Laurent Véron (1987)

Banach Center Publications

Linear elliptic operators with measurable coefficients

Neil S. Trudinger (1973)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Liouville theorems for a class of linear second-order operators with nonnegative characteristic form.

Kogoj, Alessia Elisabetta, Lanconelli, Ermanno (2007)

Boundary Value Problems [electronic only]

Local energy decay for several evolution equations on asymptotically euclidean manifolds

Jean-François Bony, Dietrich Häfner (2012)

Annales scientifiques de l'École Normale Supérieure

Let $P$ be a long range metric perturbation of the Euclidean Laplacian on $ℝ^{d}$ , $d \geq 2$ . We prove local energy decay for the solutions of the wave, Klein-Gordon and Schrödinger equations associated to $P$ . The problem is decomposed in a low and high frequency analysis. For the high energy part, we assume a non trapping condition. For low (resp. high) frequencies we obtain a general result about the local energy decay for the group $e^{i t f (P)}$ where $f$ has a suitable development at zero (resp. infinity).

Long-time behavior of small solutions to quasilinear dissipative hyperbolic equations

Albert J. Milani, Hans Volkmer (2011)

Applications of Mathematics

We give sufficient conditions for the existence of global small solutions to the quasilinear dissipative hyperbolic equation $u_{t t} + 2 u_{t} - a_{i j} (u_{t}, \nabla u) \partial_{i} \partial_{j} u = f$ corresponding to initial values and source terms of sufficiently small size, as well as of small solutions to the corresponding stationary version, i.e. the quasilinear elliptic equation $- a_{i j} (0, \nabla v) \partial_{i} \partial_{j} v = h .$ We then give conditions for the convergence, as $t \to \infty$ , of the solution of the evolution equation to its stationary state.

Lp bounds for Riesz transforms and square roots associated to second order elliptic operators.

Steve Hofmann, José María Martell (2003)

Publicacions Matemàtiques

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