EUDML

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Continuous Branches of Positive Solutions for a Class of Nonlinear Second-Order Differential Equations.

Philippe Clément — 1975

Manuscripta mathematica

Completely positive measures and Feller semigroups.

Jan Prüss; Philippe Clément — 1990

Mathematische Annalen

Global existence for a semilinear prabolic Volterra equation.

Jan Prüss; Philippe Clément — 1992

Mathematische Zeitschrift

Wasserstein metric and subordination

Philippe Clément; Wolfgang Desch — 2008

Studia Mathematica

Let $(X, d_{X})$ , $(Ω, d_{Ω})$ be complete separable metric spaces. Denote by (X) the space of probability measures on X, by $W_{p}$ the p-Wasserstein metric with some p ∈ [1,∞), and by $_{p} (X)$ the space of probability measures on X with finite Wasserstein distance from any point measure. Let $f : Ω \to_{p} (X)$ , $ω \mapsto f_{ω}$ , be a Borel map such that f is a contraction from $(Ω, d_{Ω})$ into $(_{p} (X), W_{p})$ . Let ν₁,ν₂ be probability measures on Ω with $W_{p} (ν ₁, ν ₂)$ finite. On X we consider the subordinated measures $μ_{i} = \int_{Ω} f_{ω} d ν_{i} (ω)$ . Then $W_{p} (μ ₁, μ ₂) \leq W_{p} (ν ₁, ν ₂)$ . As an application we show that the solution measures $ϱ_{α} (t)$ to the partial...

Existence and multiplicity results for a semilinear elliptic eigenvalue problem

Philippe Clément; Guido Sweers — 1987

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Homoclinic orbits for a class of infinite dimensional hamiltonian systems

Philippe Clément; Patricio Felmer; Enzo Mitidieri — 1997

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

On the regularity of abstract Cauchy problems and boundary value problems

Philippe Clément; Sylvie Guerre-Delabrière — 1998

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

Maximal regularity (in $L_{p}$ -sense) for abstract Cauchy problems of order one and boundary value problems of order two is studied. In general, regularity of the first problems implies regularity of the second ones; the converse is shown to hold if the underlying Banach space has the UMD property. A stronger notion of regularity, introduced by Sobolevskii, plays an important role in the proofs.

Some results on stochastic convolutions arising in Volterra equations perturbed by noise

Philippe Clément; Giuseppe Da Prato — 1996

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

Regularity of stochastic convolutions corresponding to a Volterra equation, perturbed by a white noise, is studied. Under suitable assumptions, hölderianity of the corresponding trajectories is proved.

Finite element analysis of a simplified stochastic Hookean dumbbells model arising from viscoelastic flows

Andrea Bonito; Philippe Clément; Marco Picasso — 2006

ESAIM: Mathematical Modelling and Numerical Analysis

A simplified stochastic Hookean dumbbells model arising from viscoelastic flows is considered, the convective terms being disregarded. A finite element discretization in space is proposed. Existence of the numerical solution is proved for small data, so as error estimates, using an implicit function theorem and regularity results obtained in [Bonito (2006) 381–398] for the solution of the continuous problem. error estimates are also derived. Numerical results with small time...