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On a Volume Constrained Variational Problem in SBV²(Ω): Part I

Ana Cristina Barroso, José Matias (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We consider the problem of minimizing the energy E ( u ) : = Ω | u ( x ) | 2 d x + S u Ω 1 + | [ u ] ( x ) | d H N - 1 ( x ) among all functions u ∈ SBV²(Ω) for which two level sets { u = l i } have prescribed Lebesgue measure α i . Subject to this volume constraint the existence of minimizers for E(.) is proved and the asymptotic behaviour of the solutions is investigated.

On analyticity of Ornstein-Uhlenbeck semigroups

Beniamin Goldys (1999)

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

Let ( R t be a transition semigroup of the Hilbert space-valued nonsymmetric Ornstein-Uhlenbeck process and let μ denote its Gaussian invariant measure. We show that the semigroup ( R t is analytic in L 2 μ if and only if its generator is variational. In particular, we show that the transition semigroup of a finite dimensional Ornstein-Uhlenbeck process is analytic if and only if the Wiener process is nondegenerate.

On Bernoulli decomposition of random variables and recent various applications

François Germinet (2007/2008)

Séminaire Équations aux dérivées partielles

In this review, we first recall a recent Bernoulli decomposition of any given non trivial real random variable. While our main motivation is a proof of universal occurence of Anderson localization in continuum random Schrödinger operators, we review other applications like Sperner theory of antichains, anticoncentration bounds of some functions of random variables, as well as singularity of random matrices.

On evolution inequalities of a modified Navier-Stokes type. I

Manfred Müller, Joachim Naumann (1978)

Aplikace matematiky

The paper present an existence theorem for a strong solution to an abstract evolution inequality where the properties of the operators involved are motivated by a type of modified Navier-Stokes equations under certain unilateral boundary conditions. The method of proof rests upon a Galerkin type argument combined with the regularization of the functional.

On F -differentiable Fredholm operators of nonstationary initial-boundary value problems

Vladimír Ďurikovič, Monika Ďurikovičová (2002)

Archivum Mathematicum

We are dealing with Dirichlet, Neumann and Newton type initial-boundary value problems for a general second order nonlinear evolution equation. Using the Fredholm operator theory we establish some sufficient conditions for Fréchet differentiability of associated operators to the given problems. With help of these results the generic properties, existence and continuous dependency of solutions for initial-boundary value problems are studied.

On first order impulsive semilinear functional differential inclusions

Mouffak Benchohra, Johnny Henderson, Sotiris K. Ntouyas (2003)

Archivum Mathematicum

In this paper the Leray-Schauder nonlinear alternative for multivalued maps combined with the semigroup theory is used to investigate the existence of mild solutions for first order impulsive semilinear functional differential inclusions in Banach spaces.

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