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$L^{p}$ -Estimates for linear elliptic systems with discontinuous coefficients

Filippo Chiarenza, Michelangelo Franciosi, Michele Frasca (1994)

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

In this Note we give $L^{p}$ estimates $(1 < p < + \infty)$ for the highest order derivatives of an elliptic system in non-divergence form with coefficients in VMO.

$L_{p}$ -estimates for solutions of Dirichlet and Neumann problems to heat equation in the wedge with edge of arbitrary codimension

Nazarov, Alexander I. (2002)

Equadiff 10

$L_{p}$ -estimates for SPDE with discontinuous coefficients in domains.

Kim, Kyeong-Hun (2005)

Electronic Journal of Probability [electronic only]

$L^{p}$ -inequalities for the laplacian and unique continuation

W. O. Amrein, A. M. Berthier, V. Georgescu (1981)

Annales de l'institut Fourier

We prove an inequality of the type $∥ | x |^{r_{f}} ∥_{L^{p} (R^{n})} \leq c (n, p, q, r) ∥ | x |^{τ + μ} Δ f ∥_{L^{q} (R^{n})} .$ This is then used to derive the unique continuation property for the differential inequality $| Δ f (x) | \leq | v (x) | | f (x) |$ under suitable local integrability assumptions on the function $v$ .

$L^{P}$ -uniqueness for infinite dimensional symmetric Kolmogorov operators : the case of variable diffusion coefficients

Vitali Liskevich, Michael Röckner, Zeev Sobol, Oleksiy Us (2001)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Large deviations and support results for nonlinear Schrödinger equations with additive noise and applications

Éric Gautier (2005)

ESAIM: Probability and Statistics

Sample path large deviations for the laws of the solutions of stochastic nonlinear Schrödinger equations when the noise converges to zero are presented. The noise is a complex additive gaussian noise. It is white in time and colored in space. The solutions may be global or blow-up in finite time, the two cases are distinguished. The results are stated in trajectory spaces endowed with topologies analogue to projective limit topologies. In this setting, the support of the law of the solution is also...

Large deviations and support results for nonlinear Schrödinger equations with additive noise and applications

Éric Gautier (2010)

ESAIM: Probability and Statistics

Sample path large deviations for the laws of the solutions of stochastic nonlinear Schrödinger equations when the noise converges to zero are presented. The noise is a complex additive Gaussian noise. It is white in time and colored in space. The solutions may be global or blow-up in finite time, the two cases are distinguished. The results are stated in trajectory spaces endowed with topologies analogue to projective limit topologies. In this setting, the support of the law of the solution is...

Large time behavior for nonlinear higher order convection–diffusion equations

Mahmoud Qafsaoui (2006)

Annales de l'I.H.P. Analyse non linéaire

Large time behavior for solutions of nonlinear parabolic problems with sign-changing measure data.

Petitta, Francesco (2008)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Large time behavior of the solution to an initial-boundary value problem with mixed boundary conditions for a nonlinear integro-differential equation

Temur Jangveladze, Zurab Kiguradze (2011)

Open Mathematics

Large time behavior of the solution to the nonlinear integro-differential equation associated with the penetration of a magnetic field into a substance is studied. Furthermore, the rate of convergence is given. Initial-boundary value problem with mixed boundary conditions is considered.

Large time behaviour of moments of solution of parabolic differential equations with random coefficients

L. Pastur (1991/1992)

Séminaire Équations aux dérivées partielles (Polytechnique)

Le problème de Pompeiu

Robert Dalmasso (1998/1999)

Séminaire de théorie spectrale et géométrie

L...-Error Estimate for an Approximation of a Parabolic Variational Inequality.

Alfredo Fetter (1986/1987)

Numerische Mathematik

Les problèmes inverses de diffusion pour les perturbations dépendant du temps

V. Petkov (1987/1988)

Séminaire Équations aux dérivées partielles (Polytechnique)

Lifshitz tails for some non monotonous random models

Frédéric Klopp, Shu Nakamura (2007/2008)

Séminaire Équations aux dérivées partielles

In this talk, we describe some recent results on the Lifshitz behavior of the density of states for non monotonous random models. Non monotonous means that the random operator is not a monotonous function of the random variables. The models we consider will mainly be of alloy type but in some cases we also can apply our methods to random displacement models.

Limite de la solution de ut - ∆um + div F(u) = 0 lorsque m --> ∞.

Philippe Bénilan, Noureddine Igbida (2000)

Revista Matemática Complutense

Dans cette article, on étudie la limite lorsque m --> ∞ de la solution du problème de Cauchy ut - ∆um + div F(u) = 0 sur un ouvert Omega avec des conditions aux bords de type Dirichlet et une donnée initiale u0 ≥ 0.

Linear elliptic equations with BMO coefficients

Menita Carozza, Gioconda Moscariello, Antonia Passarelli di Napoli (1999)

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

We prove an existence and uniqueness theorem for the Dirichlet problem for the equation $div (a (x) \nabla u) = div f$ in an open cube $Ω \subset R^{N}$ , when $f$ belongs to some $L^{p} (Ω)$ , with $p$ close to 2. Here we assume that the coefficient $a$ belongs to the space BMO( $Ω$ ) of functions of bounded mean oscillation and verifies the condition $a (x) \geq λ_{0} > 0$ for a.e. $x \in Ω$ .

Linear instability implies nonlinear instability for various types of viscous boundary layers

B. Desjardins, E. Grenier (2003)

Annales de l'I.H.P. Analyse non linéaire

Linear neutral partial differential equations: A semigroup approach.

Nagel, Rainer, Nguyen Thieu Huy (2003)

International Journal of Mathematics and Mathematical Sciences

Linear parabolic problems involving measures.

Herbert Amann (2001)

RACSAM

Desarrollamos una teoría general para la resolución de ecuaciones lineales de evolución de la forma ü + Au = μ sobre R+, donde -A es el generador infinitesimal de un semigrupo analítico fuertemente continuo y μ es una medida de Radón con valores en un espacio de Banach. Utilizamos la teoría de interpolación-extrapolación de espacios y el teorema de representación de Riesz para tales medidas.Los resultados abstractos son ilustrados mediante aplicaciones a problemas de valor inicial parabólicos de...

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