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Displaying 21 – 40 of 40

On radial limit functions for entire solutions of second order elliptic equations in R2.

André Boivin, Peter V. Paramonov (1998)

Publicacions Matemàtiques

Given a homogeneous elliptic partial differential operator L of order two with constant complex coefficients in R2, we consider entire solutions of the equation Lu = 0 for whichlimr→∞ u(reiφ) =: U(eiφ)exists for all φ ∈ [0; 2π) as a finite limit in C. We characterize the possible "radial limit functions" U. This is an analog of the work of A. Roth for entire holomorphic functions. The results seems new even for harmonic functions.

On splitting up singularities of fundamental solutions to elliptic equations in ℂ2

T. Savina (2007)

Open Mathematics

It is known that the fundamental solution to an elliptic differential equation with analytic coefficients exists, is determined up to the kernel of the differential operator, and has singularities on characteristics of the equation in ℂ2. In this paper we construct a representation of fundamental solution as a sum of functions, each of those has singularity on a single characteristic.

On the Abel basis property of the system of root vector-functions of degenerate elliptic differential operators with singular matrix coefficients.

Boimatov, K.Kh. (2006)

Sibirskij Matematicheskij Zhurnal

On the continuity of principal eigenvalues for boundary value problems with indefinite weight function with respect to radiusof balls in $ℝ^{N}$ .

Afrouzi, Ghasem Alizadeh (2002)

International Journal of Mathematics and Mathematical Sciences

On the existence of a positive solution for a semilinear elliptic equation in the upper half space.

Chen, Shaowei, Li, Yongqing (2002)

Abstract and Applied Analysis

On the existence of multiple solutions for a class of nonlinear boundary value problems

Antonio Ambrosetti (1973)

Rendiconti del Seminario Matematico della Università di Padova

On the Hölder continuity of solutions of second order elliptic equations in two variables

L. C. Piccinini, S. Spagnolo (1972)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

On the interior smoothness of solutions to second-order elliptic equations.

Gushchin, A.K. (2005)

Sibirskij Matematicheskij Zhurnal

On the Martin compactification of a bounded Lipschitz domain in a riemannian manifold

John C. Taylor (1978)

Annales de l'institut Fourier

The Martin compactification of a bounded Lipschitz domain $D \subset R^{n}$ is shown to be $\overline{D}$ for a large class of uniformly elliptic second order partial differential operators on $D$ .Let $X$ be an open Riemannian manifold and let $M \subset X$ be open relatively compact, connected, with Lipschitz boundary. Then $\overline{M}$ is the Martin compactification of $M$ associated with the restriction to $M$ of the Laplace-Beltrami operator on $X$ . Consequently an open Riemannian manifold $X$ has at most one compactification which is a compact Riemannian...

On the Neumann problem with L¹ data

J. Chabrowski (2007)

Colloquium Mathematicae

We investigate the solvability of the linear Neumann problem (1.1) with L¹ data. The results are applied to obtain existence theorems for a semilinear Neumann problem.

On the oscillation of forced second order mixed-nonlinear elliptic equations

Zhiting Xu (2010)

Annales Polonici Mathematici

Oscillation theorems are established for forced second order mixed-nonlinear elliptic differential equations ⎧ ${d i v (A (x) | | \nabla y | |}^{p - 1} {\nabla y) + ⟨ b (x), | | \nabla y | |}^{p - 1} \nabla y ⟩ + C (x, y) = e (x)$ , ⎨ ⎩ $C (x, y) = {c (x) | y |}^{p - 1} y + \sum_{i = 1}^{m} c_{i} (x) {| y |}^{p_{i} - 1} y$ under quite general conditions. These results are extensions of the recent results of Sun and Wong, [J. Math. Anal. Appl. 334 (2007)] and Zheng, Wang and Han [Appl. Math. Lett. 22 (2009)] for forced second order ordinary differential equations with...

On the Principal Eigenvalue of a Second Order Linear Elliptic Problem with an Indefinite Weight Function.

Peter Hess (1982)

Mathematische Zeitschrift

On the principal eigenvalue of elliptic operators in $ℝ^{N}$ and applications

Henry Berestycki, Luca Rossi (2006)

Journal of the European Mathematical Society

Two generalizations of the notion of principal eigenvalue for elliptic operators in $ℝ^{N}$ are examined in this paper. We prove several results comparing these two eigenvalues in various settings: general operators in dimension one; self-adjoint operators; and “limit periodic” operators. These results apply to questions of existence and uniqueness for some semilinear problems in the whole space. We also indicate several outstanding open problems and formulate some conjectures.

On the Principal Eigenvalues of Indefinite Elliptic Problems.

W. Allegretto (1987)

Mathematische Zeitschrift

On the Uniform Decay of the Local Energy

Vodev, Georgi (1999)

Serdica Mathematical Journal

It is proved in [1],[2] that in odd dimensional spaces any uniform decay of the local energy implies that it must decay exponentially. We extend this to even dimensional spaces and to more general perturbations (including the transmission problem) showing that any uniform decay of the local energy implies that it must decay like O(t^(−2n) ), t ≫ 1 being the time and n being the space dimension.

On the uniqueness of the second bound state solution of a semilinear equation

Carmen Cortázar, Marta García-Huidobro, Cecilia S. Yarur (2009)

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

On Uniqueness of Boundary Values of Solutions of a Problem Arising in Plasma Physics.

Moshe Marcus (1985)

Mathematische Zeitschrift

Optimal $L^{p}$ -properties of Green’s functions for non-divergence elliptic equations in two dimensions

Gioconda Moscariello, Carlo Sbordone (2005)

Studia Mathematica

A sharp integrability result for non-negative adjoint solutions to planar non-divergence elliptic equations is proved. A uniform estimate is also given for the Green's function.

Optimal regularity for the pseudo infinity Laplacian

Julio D. Rossi, Mariel Saez (2007)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we find the optimal regularity for viscosity solutions of the pseudo infinity Laplacian. We prove that the solutions are locally Lipschitz and show an example that proves that this result is optimal. We also show existence and uniqueness for the Dirichlet problem.

Orlicz spaces, α-decreasing functions, and the Δ₂ condition

Gary M. Lieberman (2004)

Colloquium Mathematicae

We prove some quantitatively sharp estimates concerning the Δ₂ and ∇₂ conditions for functions which generalize known ones. The sharp forms arise in the connection between Orlicz space theory and the theory of elliptic partial differential equations.

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