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Displaying 121 – 140 of 324

The interface crack with Coulomb friction between two bonded dissimilar elastic media

Hiromichi Itou, Victor A. Kovtunenko, Atusi Tani (2011)

Applications of Mathematics

We study a model of interfacial crack between two bonded dissimilar linearized elastic media. The Coulomb friction law and non-penetration condition are assumed to hold on the whole crack surface. We define a weak formulation of the problem in the primal form and get the equivalent primal-dual formulation. Then we state the existence theorem of the solution. Further, by means of Goursat-Kolosov-Muskhelishvili stress functions we derive convergent expansions of the solution near the crack tip.

The inverse problem for elliptic equations from Dirichlet to Neumann map in multiply connected domains.

Wen, Guochun, Xu, Zuoliang, Yang, Fengmin (2009)

Boundary Value Problems [electronic only]

The $L^{p}$ -Helmholtz projection in finite cylinders

Tobias Nau (2015)

Czechoslovak Mathematical Journal

In this article we prove for $1 < p < \infty$ the existence of the $L^{p}$ -Helmholtz projection in finite cylinders $Ω$ . More precisely, $Ω$ is considered to be given as the Cartesian product of a cube and a bounded domain $V$ having $C^{1}$ -boundary. Adapting an approach of Farwig (2003), operator-valued Fourier series are used to solve a related partial periodic weak Neumann problem. By reflection techniques the weak Neumann problem in $Ω$ is solved, which implies existence and a representation of the $L^{p}$ -Helmholtz projection as...

The Landau-Lifshitz equation with the external field - a new extension for harmonic maps with values in S2.

Min-Chun Hong (1995)

Mathematische Zeitschrift

The Lane-Emden Function and Nonlinear Eigenvalues Problems

Ould Ahmed Izid Bih Isselkou (2009)

Annales de la faculté des sciences de Toulouse Mathématiques

We consider a semilinear elliptic eigenvalues problem on a ball of $ℜ^{n}$ and show that all the eigenfunctions and eigenvalues, can be obtained from the Lane-Emden function.

The laplacian and the discrete laplacian

Z. Ditzian (1989)

Compositio Mathematica

The Lazer-McKenna conjecture for radial solutions in the $ℝ^{N}$ ball.

Castro, Alfonso, Gadam, Sudhasree (1993)

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

The least eigenvalues of nonhomogeneous degenerated quasilinear eigenvalue problems

Pavel Drábek (1995)

Mathematica Bohemica

We prove the existence of the least positive eigenvalue with a corresponding nonnegative eigenfunction of the quasilinear eigenvalue problem $\begin{matrix} - div (a (x, u) | |^{p - 2} \nabla u) = & {λ b (x, u) | u |}^{p - 2} u in Ω, u = & 0 on \partial Ω, \end{matrix}$ where $Ω$ is a bounded domain, $p > 1$ is a real number and $a (x, u)$ , $b (x, u)$ satisfy appropriate growth conditions. Moreover, the coefficient $a (x, u)$ contains a degeneration or a singularity. We work in a suitable weighted Sobolev space and prove the boundedness of the eigenfunction in $L^{\infty} (Ω)$ . The main tool is the investigation of the associated homogeneous eigenvalue problem and an application...

The Lévy laplacian and differential operators of 2-nd order in Hilbert spaces

Roman Lávička (1998)

Commentationes Mathematicae Universitatis Carolinae

We shall show that every differential operator of 2-nd order in a real separable Hilbert space can be decomposed into a regular and an irregular operator. Then we shall characterize irregular operators and differential operators satisfying the maximum principle. Results obtained for the Lévy laplacian in [3] will be generalized for irregular differential operators satisfying the maximum principle.

The limiting equation for Neumann Laplacians on shrinking domains.

Saito, Yoshimi (2000)

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

The Lippman-Schwinger equation treated as a characteristic Cauchy problem

A. Melin (1988/1989)

Séminaire Équations aux dérivées partielles (Polytechnique)

The local structure of Nodal set of solutions of Schrödinger equation on Riemannian 3-manifolds.

Jingyi Chen (1994)

Manuscripta mathematica

The low energy expansion in nonrelativistic scattering theory

S. Albeverio, F. Gesztesy, R. Høegh-Krohn (1982)

Annales de l'I.H.P. Physique théorique

The L.P.D.E.M., a mixed finite difference method for elliptic problems.

M. Jai, G. Bayada, M. Chambat (1992)

Numerische Mathematik

The magnetic Schrödinger operator and reverse Hölder class

Zhongwei Shen (1996)

Journées équations aux dérivées partielles

The maximum principle for equations with composite coefficients.

Lieberman, Gary M. (2000)

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

The mean curvature measure

Quiyi Dai, Neil S. Trudinger, Xu-Jia Wang (2012)

Journal of the European Mathematical Society

We assign a measure to an upper semicontinuous function which is subharmonic with respect to the mean curvature operator, so that it agrees with the mean curvature of its graph when the function is smooth. We prove that the measure is weakly continuous with respect to almost everywhere convergence. We also establish a sharp Harnack inequality for the minimal surface equation, which is crucial for our proof of the weak continuity. As an application we prove the existence of weak solutions to the...

The mean curvature of a Lipschitz continuous manifold

Elisabetta Barozzi, Eduardo Gonzalez, Umberto Massari (2003)

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

The paper is devoted to the description of some connections between the mean curvature in a distributional sense and the mean curvature in a variational sense for several classes of non-smooth sets. We prove the existence of the mean curvature measure of $\partial E$ by using a technique introduced in [4] and based on the concept of variational mean curvature. More precisely we prove that, under suitable assumptions, the mean curvature measure of $\partial E$ is the weak limit (in the sense of distributions) of the mean...

The method of fictitious domains in the Signorini problem.

Stepanov, V.D., Khludnev, A.M. (2003)

Sibirskij Matematicheskij Zhurnal

The method of fictitious right-hand sides

Milan Práger (1984)

Aplikace matematiky

The paper deals with the application of a fast algorithm for the solution of finite-difference systems for boundary-value problems on a standard domain (e.g. on a rectangle) to the solution of a boundary-value problem on a domain of general shape contained in the standard domain. A simple iterative procedure is suggested for the determination of fictitious right-hand sides for the system on the standard domain so that its solution is the desired one. Under the assumptions that are usual for matrices...

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