Results 301 to 310 of about 22,885,588 (357)

On the C1 regularity of solutions to divergence form elliptic systems with dini-continuous coefficients

Chinese Annals of Mathematics. Series B, 2016
The author proves C1 regularity of solutions to divergence form elliptic systems with Dini-continuous coefficients.
Yanyan Li
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Overdetermined Elliptic Systems

Foundations of Computational Mathematics, 2005
We consider linear overdetermined systems of partial differential equations. We show that the introduction of weights classically used for the definition of ellipticity is not necessary, as any system that is elliptic with respect to some weights becomes elliptic without weights during its completion to involution.
Katsiaryna Krupchyk, Werner M. Seiler, Jukka Tuomela   +2 more
openaire   +1 more source

Global well-posedness and stability of constant equilibria in parabolic–elliptic chemotaxis systems without gradient sensing

Nonlinearity, 2019
This paper deals with a Keller–Segel type parabolic–elliptic system involving nonlinear diffusion and chemotaxis in a smoothly bounded domain , , under no-flux boundary conditions.
Jaewook Ahn, Changwook Yoon
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Asymptotics for Semilinear Elliptic Systems

Canadian Mathematical Bulletin, 1991
AbstractA class of weakly coupled systems of semilinear elliptic partial differential equations is considered in an exterior domain in ℝN, N > 3. Necessary and sufficient conditions are given for the existence of a positive solution (componentwise) with the asymptotic decay u(x) = O(|x|2-N) as |x| —> ∞.
Noussair, Ezzat S., Swanson, Charles A.
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Positive splutions of semilinear elliptic systems

Communications in Partial Differential Equations, 1992
We investigate the existence of positive solutions of a Dirichlet problem for the system -A. =f(u),-Av =g(u) in a bounded convex domain 0 of IRN with smooth boundary. In particular L" a priori bounds are obtained in the same spirit as in De Figueiredo - Lions - Nussbaum [7].
MITIDIERI, ENZO, CLEMENT PH, DE FIGUEIREDO D.   +2 more
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Proportionality of Components, Liouville Theorems and a Priori Estimates for Noncooperative Elliptic Systems

Archive for Rational Mechanics and Analysis, 2013
We study qualitative properties of positive solutions of noncooperative, possibly nonvariational, elliptic systems. We obtain new classification and Liouville type theorems in the whole Euclidean space, as well as in half-spaces, and deduce a priori ...
Alexandre Montaru, B. Sirakov, P. Souplet   +2 more
semanticscholar   +1 more source

Singularly perturbed elliptic systems

Nonlinear Analysis: Theory, Methods & Applications, 2006
The authors prove the existence of a family of positive solutions for two coupled nonlinear stationary Schrödinger equations, concentrating at a point in the limit. In some cases the location of the concentration point is given in terms of the potential functions of the stationary Schrödinger equations.
Alves, Claudianor O., Soares, Sérgio H. M.   +1 more
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Nonlinear Elliptic Systems

2018
This chapter is devoted to the study of systems of nonlinear elliptic equations taking into account their internal structure. Separately, the study concerns systems fully depending on the gradient of the solutions, systems that are subject to the method of subsolution–supersolution which in the case of systems takes a special form, and systems with a ...
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Nonlinear Elliptic Systems

2012
We present a maximum principle of W. Jager for the H-surface system in Section 1. Then we prove the fundamental gradient estimate of E. Heinz for nonlinear elliptic systems of differential equations in Section 2. Global estimates are established in Section 3.
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Strongly elliptic systems and boundary integral equations

Mathematical Gazette, 2000
M. Mudge
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