The Pohozaev-type inequalities and their applications for a kind of elliptic equation (system)
Boundary Value Problems, 2020 In this paper, we first derive a new kind of Pohozaev-type inequalities for p-Laplacian equations in a more general class of non-star-shaped domains, and then we take two examples and their graphs to explain the shape of the new kind of the non-star ...
Bingyu Kou, Tianqing An, Zeyan Wang
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Distributed Control of Systems Governed by a General Class of Quasilinear Elliptic Equations
Journal of Differential Equations, 1993 Let \(\Omega\) be a bounded open subset of \(\mathbb{R}^ N\) with Lipschitz continuous boundary; let \(a: \Omega\times \mathbb{R}^ N\to \mathbb{R}^ N\), \(a_ 0: \Omega\times\mathbb{R}\to \mathbb{R}\) be two Carathéodory functions, \(C^ 1\) in the second variable, such that \[ \sum_{i,j=1}^ N \partial_{N+i} a_ j (.,\eta) \xi_ i\xi_ j\geq \Lambda_ 1(k+| \
Casas, E., Fernandez, L.A.
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Multivalued solutions of multidimensional linear equations of heat conduction and rivertons
Известия высших учебных заведений. Поволжский регион: Физико-математические науки, 2021 Background. The article considers the problem of calculating multivalued solutions of multidimensional linear parabolic equations. Solutions for this type of equations of heat conductivity in dimension d > 2 were not previously known and represent an ...
V.M. Zhuravlev, V.M. Morozov
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Alexandria Engineering Journal, 2020 In this work, a cubic B-spline method based on finite difference and meshless approaches for solving 2D generalized telegraph equations in irregular single and multi-connected domains is presented.
Sergiy Reutskiy +3 more
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New elliptic system and global solutions for the constraints equations in General relativity [PDF]
Communications in Mathematical Physics, 1971 By a new choice of the arbitrarily given quantities on an initial 3-manifold we reduce the system of constraints, in General Relativity, to an elliptic system of four equations, the coefficients of which have a simple geometric interpretation on the 3-manifold. The system seems well suited for a global study and some results are given in this direction.
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On Critical Behaviour in Systems of Hamiltonian Partial Differential Equations [PDF]
, 2015 We study the critical behaviour of solutions to weakly dispersive Hamiltonian systems considered as perturbations of elliptic and hyperbolic systems of hydrodynamic type with two components.
Klein, Christian +13 more
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Generalized Hitchin Systems and the Knizhnik–zamolodchikov–bernard Equation on Ellipic Curves [PDF]
Letters in Mathematical Physics, 1997 Knizhnik-Zamolodchikov-Bernard (KZB) equation on an elliptic curve with a marked point is derived by the classical Hamiltonian reduction and further quantization. We consider classical Hamiltonian systems on cotangent bundle to the loop group $L(GL(N,{\bf C}))$ extended by the shift operators, to be related to the elliptic module.
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Knot points of a double-covariant system of elliptic equations and preferred frames in general relativity [PDF]
Journal of Physics A: Mathematical and General, 2002 The elliptic system of equations, which is general-covariant and locally SU(2)-covariant, is investigated. The new condition of the Dirichlet problem solvability and the condition of zeros absence for solutions are obtained for this system, which contains in particular case the Sen-Witten equation.
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Metric Based Upscaling for Partial Differential Equations with a Continuum of Scales [PDF]
, 2007 Numerical upscaling of problems with multiple scale structures have attracted increasing attention in recent years. In particular, problems with non-separable scales pose a great challenge to mathematical analysis and simulation.
Zhang, Lei
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Extrapolated elliptic regularity and application to the van Roosbroeck system of semiconductor equations [PDF]
, 2020 In this paper we present a general extrapolated elliptic regularity result for second order differential operators in divergence form on fractional Sobolev-type spaces of negative order Xs-1,qD(Ω) for s > 0 small, including mixed boundary conditions and ...
Meinlschmidt, Hannes, Rehberg, Joachim
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