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Displaying 221 – 240 of 1370

Bounded weak solutions to nonlinear elliptic equations.

El Hachimi, Abderrahmane, Igbida, Jaoud (2009)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

Boundedness and integrability properties of weak solutions of quasilinear elliptic systems.

Michael Meier (1982)

Journal für die reine und angewandte Mathematik

Boundedness and pointwise differentiability of weak solutions to quasi-linear elliptic differential equations and variational inequalities

Jana Ježková (1994)

Commentationes Mathematicae Universitatis Carolinae

The local boundedness of weak solutions to variational inequalities (obstacle problem) with the linear growth condition is obtained. Consequently, an analogue of a theorem by Reshetnyak about a.eḋifferentiability of weak solutions to elliptic divergence type differential equations is proved for variational inequalities.

Bounds and numerical results for homogenized degenerated $p$ -Poisson equations

Johan Byström, Jonas Engström, Peter Wall (2004)

Applications of Mathematics

In this paper we derive upper and lower bounds on the homogenized energy density functional corresponding to degenerated $p$ -Poisson equations. Moreover, we give some non-trivial examples where the bounds are tight and thus can be used as good approximations of the homogenized properties. We even present some cases where the bounds coincide and also compare them with some numerical results.

Branching processes, random trees and superprocesses.

Le Gall, Jean-François (1998)

Documenta Mathematica

BSDEs with random terminal time and semilinear elliptic PDEs in divergence form

Andrzej Rozkosz (2005)

Studia Mathematica

We study connections between Sobolev space solutions of the Dirichlet problem for semilinear second order elliptic equations in divergence form and solutions of backward stochastic differential equations with random terminal time.

Bubbling along boundary geodesics near the second critical exponent

Manuel del Pino, Monica Musso, Frank Pacard (2010)

Journal of the European Mathematical Society

The role of the second critical exponent $p = (n + 1) / (n - 3)$ , the Sobolev critical exponent in one dimension less, is investigated for the classical Lane–Emden–Fowler problem $Δ u + u^{p} = 0$ , $u > 0$ under zero Dirichlet boundary conditions, in a domain $Ω$ in $ℝ^{n}$ with bounded, smooth boundary. Given $Γ$ , a geodesic of the boundary with negative inner normal curvature we find that for $p = (n + 1) / (n - 3 - ε)$ , there exists a solution $u_{ε}$ such that $| \nabla u_{ε} |^{2}$ converges weakly to a Dirac measure on $Γ$ as $ε \to 0^{+}$ , provided that $Γ$ is nondegenerate in the sense of second variations of...

$C^{1}$ -regularity of the Aronsson equation in $R^{2}$

Changyou Wang, Yifeng Yu (2008)

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

$C^{1, α}$ convergence of minimizers of a Ginzburg-Landau functional.

Lei, Yutian, Wu, Zhuoqun (2000)

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

$C^{1, α}$ local regularity for the solutions of the $p$ -Laplacian on the Heisenberg group. The case $1 + \frac{1}{\sqrt{5}} < p \leq 2$

Silvana Marchi (2003)

Commentationes Mathematicae Universitatis Carolinae

We prove the Hölder continuity of the homogeneous gradient of the weak solutions $u \in W_{loc}^{1, p}$ of the p-Laplacian on the Heisenberg group $ℋ^{n}$ , for $1 + \frac{1}{\sqrt{5}} < p \leq 2$ .

$C^{\infty}$ regularity of solutions of a quasilinear equation related to the Levi operator

G. Citti (1996)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Capacitary strong type estimates in semilinear problems

D. Adams, Michel Pierre (1991)

Annales de l'institut Fourier

We prove the equivalence of various capacitary strong type estimates. Some of them appear in the characterization of the measures $μ$ that are admissible data for the existence of solutions to semilinear elliptic problems with power growth. Other estimates are known to characterize the measures $μ$ for which the Sobolev space $W^{2, p}$ can be imbedded into $L^{p} (μ)$ . The motivation comes from the semilinear problems: simpler descriptions of admissible data are given. The proof surprisingly involves the theory of singular...

Characterizations of p-superharmonic functions on metric spaces

Anders Björn (2005)

Studia Mathematica

We show the equivalence of some different definitions of p-superharmonic functions given in the literature. We also provide several other characterizations of p-superharmonicity. This is done in complete metric spaces equipped with a doubling measure and supporting a Poincaré inequality. There are many examples of such spaces. A new one given here is the union of a line (with the one-dimensional Lebesgue measure) and a triangle (with a two-dimensional weighted Lebesgue measure). Our results also...

Compact embedding of a degenerate Sobolev space and existence of entire solutions to a semilinear equation for a Grushin-type operator

Francesca Lascialfari, David Pardo (2002)

Rendiconti del Seminario Matematico della Università di Padova

Compacteness methods for certain degenerate elliptic systems.

Lihe Wang (1993)

Manuscripta mathematica

Currently displaying 221 – 240 of 1370