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Displaying 501 – 520 of 920

On positive Rockland operators

Pascal Auscher, A. ter Elst, Derek Robinson (1994)

Colloquium Mathematicae

Let G be a homogeneous Lie group with a left Haar measure dg and L the action of G as left translations on $L_{p} (G; d g)$ . Further, let H = dL(C) denote a homogeneous operator associated with L. If H is positive and hypoelliptic on $L_{2}$ we prove that it is closed on each of the $L_{p}$ -spaces, p ∈ 〈 1,∞〉, and that it generates a semigroup S with a smooth kernel K which, with its derivatives, satisfies Gaussian bounds. The semigroup is holomorphic in the open right half-plane on all the $L_{p}$ -spaces, p ∈ [1,∞]. Further extensions...

On positive solutions of semilinear elliptic problems

Pavol Quittner (1989)

Commentationes Mathematicae Universitatis Carolinae

On quasilinear elliptic equations in domains with conical boundary points.

Manfred Dobrowolski (1989)

Journal für die reine und angewandte Mathematik

On Quasilinear Elliptic Systems of Diagonal Form.

Per-Anders Ivert (1980)

Mathematische Zeitschrift

On solvability of boundary value problem for elliptic equations with Bitsadze-Samarskij condition.

Chabrowski, J.H. (1988)

International Journal of Mathematics and Mathematical Sciences

On some improperly posed problem for a degenerate nonlinear parabolic equation.

Hayasida, K. (2000)

Zeitschrift für Analysis und ihre Anwendungen

On some $L^{p}$ -estimates for solutions of elliptic equations in unbounded domains

Sara Monsurrò, Maria Transirico (2015)

Mathematica Bohemica

In this review article we present an overview on some a priori estimates in $L^{p}$ , $p > 1$ , recently obtained in the framework of the study of a certain kind of Dirichlet problem in unbounded domains. More precisely, we consider a linear uniformly elliptic second order differential operator in divergence form with bounded leading coeffcients and with lower order terms coefficients belonging to certain Morrey type spaces. Under suitable assumptions on the data, we first show two $L^{p}$ -bounds, $p > 2$ , for the solution...

On some nonlinear elliptic systems with coercive perturbation in RN.

Said El Manouni, Abdelfattah Touzani (2003)

Revista Matemática Complutense

A nonlinear elliptic system involving the p-Laplacian is considered in the whole RN. Existence of nontrivial solutions is obtained by applying critical point theory; also a regularity result is established.

On Squeezing and Flow of Energy for Nonlinear Wave Equations.

S.B. Kuksin (1995)

Geometric and functional analysis

On the boundedness of the mapping $f \to | f |$ in Besov spaces

Patrick Oswald (1992)

Commentationes Mathematicae Universitatis Carolinae

For $1 \leq p \leq \infty$ , precise conditions on the parameters are given under which the particular superposition operator $T : f \to | f |$ is a bounded map in the Besov space $B_{p, q}^{s} (R^{1})$ . The proofs rely on linear spline approximation theory.

On the Charney Conjecture of Data Assimilation Employing Temperature Measurements Alone: The Paradigm of 3D Planetary Geostrophic Model

Aseel Farhat, Evelyn Lunasin, Edriss S. Titi (2016)

Mathematics of Climate and Weather Forecasting

Analyzing the validity and success of a data assimilation algorithmwhen some state variable observations are not available is an important problem in meteorology and engineering. We present an improved data assimilation algorithm for recovering the exact full reference solution (i.e. the velocity and temperature) of the 3D Planetary Geostrophic model, at an exponential rate in time, by employing coarse spatial mesh observations of the temperature alone. This provides, in the case of this paradigm,...

On the Dirichlet problem for quasilinear elliptic second order equations with triple degeneracy and singularity in a domain with a boundary conical point.

Borsuk, Michail, Portnyagin, Dmitriy (1999)

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

On the Euler equations of incompressible perfect fluids

R. Temam (1974/1975)

Séminaire Équations aux dérivées partielles (Polytechnique)

On the existence of a classical solution of a mixed boundary problem for a second order one-dimensional hyperbolic equation. II.

Lažetić, Nebojša L. (1998)

Publications de l'Institut Mathématique. Nouvelle Série

On the existence of a fundamental solution for a parabolic differential equation with unbounded coefficients

P. Besala (1975)

Annales Polonici Mathematici

On the Fejér-F. Riesz inequality in $L^{p}$

Yoram Sagher (1977)

Studia Mathematica

On the global well-posedness of the Boussinesq system with zero viscosity

Taoufik Hmidi (2007/2008)

Séminaire Équations aux dérivées partielles

In this paper we prove the global well-posedness of the two-dimensional Boussinesq system with zero viscosity for rough initial data.

On the Klainerman–Machedon conjecture for the quantum BBGKY hierarchy with self-interaction

Xuwen Chen, Justin Holmer (2016)

Journal of the European Mathematical Society

We consider the 3D quantum BBGKY hierarchy which corresponds to the $N$ -particle Schrödinger equation. We assume the pair interaction is $N^{3 β - 1} V (B^{β})$ . For the interaction parameter $β \in (0, 2 / 3)$ , we prove that, provided an energy bound holds for solutions to the BBKGY hierarchy, the $N \to \infty$ limit points satisfy the space-time bound conjectured by S. Klainerman and M. Machedon [45] in 2008. The energy bound was proven to hold for $β \in (0, 3 / 5)$ in [28]. This allows, in the case $β \in (0, 3 / 5)$ , for the application of the Klainerman–Machedon uniqueness theorem...

On the local behaviour of solutions of a certain class of doubly nonlinear parabolic equations.

Vincenzo Vespri (1992)

Manuscripta mathematica

On the long-time behaviour of solutions of the p-Laplacian parabolic system

Paweł Goldstein (2008)

Colloquium Mathematicae

Convergence of global solutions to stationary solutions for a class of degenerate parabolic systems related to the p-Laplacian operator is proved. A similar result is obtained for a variable exponent p. In the case of p constant, the convergence is proved to be $¹_{l o c}$ , and in the variable exponent case, L² and $W^{1, p (x)}$ -weak.

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