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Displaying 81 – 100 of 504

Elliptic problems in generalized Orlicz-Musielak spaces

Piotr Gwiazda, Piotr Minakowski, Aneta Wróblewska-Kamińska (2012)

Open Mathematics

We consider a strongly nonlinear monotone elliptic problem in generalized Orlicz-Musielak spaces. We assume neither a Δ2 nor ∇2-condition for an inhomogeneous and anisotropic N-function but assume it to be log-Hölder continuous with respect to x. We show the existence of weak solutions to the zero Dirichlet boundary value problem. Within the proof the L ∞-truncation method is coupled with a special version of the Minty-Browder trick for non-reflexive and non-separable Banach spaces.

Elliptic problems with integral diffusion

Yannick Sire (2011/2012)

Séminaire Laurent Schwartz — EDP et applications

In this paper, we review several recent results dealing with elliptic equations with non local diffusion. More precisely, we investigate several problems involving the fractional laplacian. Finally, we present a conformally covariant operator and the associated singular and regular Yamabe problem.

Elliptic problems with nonmonotone discontinuities at resonance.

Nikolaos, Halidias (2002)

Abstract and Applied Analysis

Elliptic quasi-variational inequalities and application to a non-stationary problem in hydraulics

Avner Friedman, Robert Jensen (1976)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Elliptic regularity and essential self-adjointness of Dirichlet operators on $ℝ^{n}$

Vladimir I. Bogachev, Nicolai V. Krylov, Michael Röckner (1997)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Elliptic resonance problems with unequal limits at infinity.

Martin Schechter (1994)

Mathematische Annalen

Elliptische Differentialgleichungen mit variablen Koeffizienten in Gebieten mit unbeschränktem Rand.

Volker Vogelsang (1974/1975)

Manuscripta mathematica

Embedded eigenvalues and resonances of Schrödinger operators with two channels

Xue Ping Wang (2007)

Annales de la faculté des sciences de Toulouse Mathématiques

In this article, we give a necessary and sufficient condition in the perturbation regime on the existence of eigenvalues embedded between two thresholds. For an eigenvalue of the unperturbed operator embedded at a threshold, we prove that it can produce both discrete eigenvalues and resonances. The locations of the eigenvalues and resonances are given.

Embedding and a priori wavelet-adaptivity for Dirichlet problems

Andreas Rieder (2000)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Embedding and a priori wavelet-adaptivity for Dirichlet problems

Andreas Rieder (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The accuracy of the domain embedding method from [A. Rieder, Modél. Math. Anal. Numér.32 (1998) 405-431] for the solution of Dirichlet problems suffers under a coarse boundary approximation. To overcome this drawback the method is furnished with an a priori (static) strategy for an adaptive approximation space refinement near the boundary. This is done by selecting suitable wavelet subspaces. Error estimates and numerical experiments validate the proposed adaptive scheme. In contrast to similar,...

Embedding of open riemannian manifolds by harmonic functions

Robert E. Greene, H. Wu (1975)

Annales de l'institut Fourier

Let $M$ be a noncompact Riemannian manifold of dimension $n$ . Then there exists a proper embedding of $M$ into $R^{2 n + 1}$ by harmonic functions on $M$ . It is easy to find $2 n + 1$ harmonic functions which give an embedding. However, it is more difficult to achieve properness. The proof depends on the theorems of Lax-Malgrange and Aronszajn-Cordes in the theory of elliptic equations.

Embedding theorems into lipschitz and BMO spaces and applications to quasilinear subelliptic differential equations.

Guozhen Lu (1996)

Publicacions Matemàtiques

En ε-uniformly convergent non-conforming finite element method for a singularly perturbed elliptic problem in two dimensions

J. J. H. Miller, S. Wang (1990)

Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

Enclosure of solutions for elliptic boundary value problems with nonmonotone discontinuous nonlinearity

Siegfried Carl (1994)

Banach Center Publications

Energies of $S^{2}$ -valued harmonic maps on polyhedra with tangent boundary conditions

A. Majumdar, J. M. Robbins, M. Zyskin (2008)

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

Énergies relaxées pour applications harmoniques

F. Bethuel (1989/1990)

Séminaire Équations aux dérivées partielles (Polytechnique)

Energy and Morse index of solutions of Yamabe type problems on thin annuli

Mohammed Ben Ayed, Khalil El Mehdi, Mohameden Ould Ahmedou, Filomena Pacella (2005)

Journal of the European Mathematical Society

We consider the Yamabe type family of problems $(P_{ε}) : - Δ u_{ε} = u_{ε}^{(n + 2) / (n - 2)}$ , $u_{ε} > 0$ in $A_{ε}$ , $u_{ε} = 0$ on $\partial A_{ε}$ , where $A_{ε}$ is an annulus-shaped domain of $ℝ^{n}$ , $n \geq 3$ , which becomes thinner as $ε \to 0$ . We show that for every solution $u_{ε}$ , the energy $\int_{A_{ε}} | \nabla u_{|}^{2}$ as well as the Morse index tend to infinity as $ε \to 0$ . This is proved through a fine blow up analysis of appropriate scalings of solutions whose limiting profiles are regular, as well as of singular solutions of some elliptic problem on $ℝ^{n}$ , a half-space or an infinite strip. Our argument also involves a Liouville type theorem...

Energy quantization and mean value inequalities for nonlinear boundary value problems

Katrin Wehrheim (2005)

Journal of the European Mathematical Society

We give a unified statement and proof of a class of well known mean value inequalities for nonnegative functions with a nonlinear bound on the Laplacian. We generalize these to domains with boundary, requiring a (possibly nonlinear) bound on the normal derivative at the boundary. These inequalities give rise to an energy quantization principle for sequences of solutions of boundary value problems that have bounded energy and whose energy densities satisfy nonlinear bounds on the Laplacian and normal...

Energy quantization for Yamabe's problem in conformal dimension.

Mahmoudi, Fethi (2006)

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

Enhanced electrical impedance tomography via the Mumford–Shah functional

Luca Rondi, Fadil Santosa (2001)

ESAIM: Control, Optimisation and Calculus of Variations

We consider the problem of electrical impedance tomography where conductivity distribution in a domain is to be reconstructed from boundary measurements of voltage and currents. It is well-known that this problem is highly illposed. In this work, we propose the use of the Mumford–Shah functional, developed for segmentation and denoising of images, as a regularization. After establishing existence properties of the resulting variational problem, we proceed by demonstrating the approach in several...

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