Results 261 to 270 of about 2,229 (304)

On the Continuous Solutions of a Degenerate Elliptic Equation

Proceedings of the London Mathematical Society, 1985
Dans cet article l'A. étudie l'équation \(-(\phi a^{ij}u_{x_ i})_{x_ j}+a^ iu_{x_ i}+a^ 0u=f\) dans \(\Omega\) où \(\phi\) est equivalent à la distance de x à \(\partial \Omega\). Il précise des conditions d'existence de solutions dont il donne la régularité.
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The Degenerate Venttsel Problem to Elliptic Equations

Journal of Mathematical Sciences, 2006
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ON DEGENERATE NONLINEAR ELLIPTIC EQUATIONS. II

Mathematics of the USSR-Sbornik, 1984
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Unique Continuation for Degenerate Elliptic Equations

1992
A famous result, first proved in ℝ2 by Carleman [C] in 1939, states that if \(V \in L_{\text{loc}}^{\infty}(\mathbb{R}^N)\) and u is a solution to Δu = Vu in a connected open set \(D \subset \mathbb{R}^N\), then u cannot vanish to infinite order at a point x 0 ∈ D unless u ≡ 0 in D.
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Existence and Multiplicity Results for a Degenerate Elliptic Equation

Acta Mathematica Sinica, English Series, 2006
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Dong, Wei, Chen, Jiantao
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Degenerate elliptic-parabolic equation

Communications in Partial Differential Equations, 1978
(1978). Degenerate elliptic-parabolic equation. Communications in Partial Differential Equations: Vol. 3, No. 11, pp. 1007-1040.
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Existence of solutions for nonlinear elliptic degenerate equations

Nonlinear Analysis: Theory, Methods & Applications, 2003
The authors study the following nonlinear elliptic problem: \[ -\operatorname{div} a(x,u,b\nabla u)- \operatorname{div}\varphi(u)+g(x,u)=f \quad\text{in } \Omega, \qquad u=0 \quad\text{on } \partial\Omega, \tag{1} \] where \(g(x,t)\) is the Carathéodory function such that for a.e. \(x\in\Omega\) and all \(t\in\mathbb R\), \(g(x,t)t\geq 0\). The goal of
Benkirane, A., Bennouna, J.
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Regular points for degenerate elliptic equations

1985
The authors study regular points for elliptic operators which are degenerate in the sense of \textit{M. K. V. Murthy} and \textit{G. Stampacchia} [Ann. Mat. Pura Appl., IV. Ser. 80, 1-122 (1968; Zbl 0185.192)]. The main tools are capacities and weighted Sobolev spaces.
BIROLI M, MARCHI, Silvana
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DEGENERATE ELLIPTIC PSEUDODIFFERENTIAL EQUATIONS OF PRINCIPAL TYPE

Mathematics of the USSR-Sbornik, 1970
This article studies pseudodifferential operators which are elliptic outside an (n - 1)-dimensional submanifold ω of a closed n-dimensional manifold Γ. It is assumed that at those points of the cotangent bundle at which the ellipticity condition is violated the gradient of the determinant of the symbol is nonzero and transversal to ω.
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The Finite Element Method for a Degenerate Elliptic Equation

SIAM Journal on Numerical Analysis, 1987
The author considers \(\Delta u+2\sigma y^{-1}u_ y=f\) \((\sigma >0)\) on \(\Omega\), \(u=0\) on \(\Gamma\), \(u_ y=0\) on \(\Gamma_ 0\), where \(\Omega\) is a bounded convex domain in the upper half-plane, \(\partial \Omega\) intersects the x-axis in \(\Gamma_ 0\) and \(\Gamma_ 1\) is the rest of \(\partial \Omega\).
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