Results 221 to 230 of about 683 (263)

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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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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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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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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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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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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On the Hölder continuity of the solutions for degenerate elliptic equations

Funkcialaj Ekvacioj, 1983
Les auteurs mettent en évidence de la régularité Hölderienne pour des solutions ''faibles'' non négatives, bornées, d'opérateurs elliptiques dégénérés de la forme: \[ L(u)=(\partial /\partial x_ i)(a_{ij}(x,u)u_{xj})-B(x,u)u^{\nu}u_{xj}-B_ 0(x,u)=0 \] avec essentiellement: \(Co u^{\tau}| \rho |^ 2\leq a_{ij}(x,u)\rho_ i\rho_ j\leq Co^{-1}u^ 2| \rho ...
Ohara, Yasuhiro, Ikebe, Nobunori
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Degenerate Parabolic and Elliptic Equations

1994
The region where the equation deteriorates is fixed for linear and semilinear degenerate equations. The cases usually discussed are that the degenerate region is on the boundary. The two approaches are often used. One is the barrier argument and another is introducing the weighted Sobolev spaces.
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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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