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Displaying 121 – 140 of 1170

An application of eigenfunctions of $p$ -Laplacians to domain separation

Herbert Gajewski (2001)

Mathematica Bohemica

We are interested in algorithms for constructing surfaces $Γ$ of possibly small measure that separate a given domain $Ω$ into two regions of equal measure. Using the integral formula for the total gradient variation, we show that such separators can be constructed approximatively by means of sign changing eigenfunctions of the $p$ -Laplacians, $p \to 1$ , under homogeneous Neumann boundary conditions. These eigenfunctions turn out to be limits of steepest descent methods applied to suitable norm quotients.

An application of subordination on harmonic function.

Al-Kharsani, H.A. (2007)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

An elliptic equation with no monotonicity condition on the nonlinearity

Gregory S. Spradlin (2006)

ESAIM: Control, Optimisation and Calculus of Variations

An elliptic PDE is studied which is a perturbation of an autonomous equation. The existence of a nontrivial solution is proven via variational methods. The domain of the equation is unbounded, which imposes a lack of compactness on the variational problem. In addition, a popular monotonicity condition on the nonlinearity is not assumed. In an earlier paper with this assumption, a solution was obtained using a simple application of topological (Brouwer) degree. Here, a more subtle degree...

An energy estimate of an exterior problem and a Liouville theorem for harmonic maps

Dong Zhang (1994)

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

An estimate on the relative Morse index for strongly indefinite functionals.

Abbondandolo, A., Felmer, P., Molina, J. (2001)

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

An existence result for minimal spheres in manifolds boundary

Edi Rosset (1990)

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

We prove the existence of a not homotopically trivial minimal sphere in a 3-manifold with boundary, obtained by deleting an open connected subset from a compact Riemannian oriented 3-manifold with boundary, having trivial second homotopy group.

An existence theorem for a non-regular variational problem.

L.M. Sibner (1983)

Manuscripta mathematica

An Existence Theorem for Harmonic Maps.

Jochen Lohkamp (1990)

Manuscripta mathematica

An Existence Theorem for Harmonic Sections.

C.M. Wood (1990)

Manuscripta mathematica

An extension of a multiplicity theorem by Ricceri with an application to a class of quasilinear equations

Francesca Faraci, Antonio Iannizzotto (2006)

Studia Mathematica

A recent multiplicity result by Ricceri, stated for equations in Hilbert spaces, is extended to a wider class of Banach spaces. Applications to nonlinear boundary value problems involving the p-Laplacian are presented.