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The Degenerate Venttsel Problem to Elliptic Equations
Journal of Mathematical Sciences, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Nonlinear elliptic problems approximating degenerate equations
Nonlinear Analysis: Theory, Methods & Applications, 1997The authors are concerned with the following problem: \[ -\text{div } ( a_{\varepsilon}(x) \nabla u) + g(x,u) = 0 \quad \text{in }\Omega, \quad u = 0 \quad \text{on }\partial \Omega, \leqno(P_{\varepsilon}) \] where \(g \) is subcritical, \(\Omega\) bounded, and the matrix \(a_{\varepsilon}\) satisfies an ellipticity condition and is assumed to ...
M. Musso, PASSASEO, Donato
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Unique Continuation for Degenerate Elliptic Equations
1992A 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 PSEUDODIFFERENTIAL EQUATIONS OF PRINCIPAL TYPE
Mathematics of the USSR-Sbornik, 1970This 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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Degenerate elliptic equations with singular nonlinearities
Calculus of Variations and Partial Differential Equations, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
CASTORINA, DANIELE +3 more
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Regular points for degenerate elliptic equations
1985The 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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Regularity for quasilinear degenerate elliptic equations
Mathematische Zeitschrift, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
DI FAZIO, Giuseppe, ZAMBONI, Pietro
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Weak regularity of degenerate elliptic equations
Lobachevskii Journal of Mathematics, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gol'dshtein, V., Ukhlov, A.
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A strongly degenerate quasilinear elliptic equation
Nonlinear Analysis: Theory, Methods & Applications, 2005zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Andreu, F., Caselles, V., Mazón, J. M.
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Existence of solutions for nonlinear elliptic degenerate equations
Nonlinear Analysis: Theory, Methods & Applications, 2003The 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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