Discrete exterior geometry approach to structure-preserving discretization of distributed-parameter port-Hamiltonian systems [PDF]
, 2011 This paper addresses the issue of structure-preserving discretization of open distributed-parameter systems with Hamiltonian dynamics. Employing the formalism of discrete exterior calculus, we introduce a simplicial Dirac structure as a discrete analogue
Seslija, Marko, +11 more
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Solvability of Iterative Classes of Nonlinear Elliptic Equations on an Exterior Domain
Axioms, 2023 This work explores the possibility that iterative classes of elliptic equations have both single and coupled positive radial solutions. Our approach is based on using the well-known Guo–Krasnoselskii and Avery–Henderson fixed-point theorems in a Banach ...
Xiaoming Wang +3 more
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Biharmonic problem in exterior domains
Comptes Rendus. Mathématique, 2003 We study here a biharmonic equation in an exterior domain of ℝ n . We give in L p
Amrouche, Chérif, Fontes, Mathieu
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Localized boundary-domain singular integral equations based on harmonic parametrix for divergence-form elliptic PDEs with variable matrix coefficients [PDF]
, 2013 This is the post-print version of the Article. The official publised version can be accessed from the links below. Copyright @ 2013 Springer BaselEmploying the localized integral potentials associated with the Laplace operator, the Dirichlet, Neumann and
Mikhailov, SE +2 more
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Positive evanescent solutions of singular elliptic problems in exterior domains
Electronic Journal of Qualitative Theory of Differential Equations, 2016 We investigate the existence of positive solutions for the following class of nonlinear elliptic problems \[\operatorname{div}(a(\|x\|)\nabla u(x))+f(x,u(x))-(u(x))^{-\alpha}\|\nabla u(x)\|^{\beta}+g(\|x\|)x\cdot\nabla u(x)=0,\] where $x\in\mathbb{R}^{n}$
Aleksandra Orpel
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The semistatic limit for Maxwell's equations in an exterior domain [PDF]
, 2005 This paper provides a $L^p$-theory for the Maxwell-system in the semistatic limit case in an exterior domain. The problem under consideration is of mixed type, since the possibly nonlinear electric conductivity vanishes on a certain subset of the domain.
Jochmann, Frank
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Analysis of positive solutions for classes of quasilinear singular problems on exterior domains
Advances in Nonlinear Analysis, 2017 We consider the ...
Chhetri Maya +2 more
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Existence and Nonexistence of Solutions to p-Laplacian Problems on Unbounded Domains
Mathematics, 2019 In this article, using a fixed point index theorem on a cone, we prove the existence and multiplicity results of positive solutions to a one-dimensional p-Laplacian problem defined on infinite intervals.
Jeongmi Jeong +2 more
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A domain decomposition method for linear exterior boundary value problems [PDF]
, 1998 In this paper, we present a domain decomposition method, based on the general theory of Steklov-Poincaré operators, for a class of linear exterior boundary value problems arising in potential theory and heat conductivity.
E.C. Hernandez +5 more
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Determinants of Laplacians in Exterior Domains
, 1999 We consider classes of simply connected planar domains which are isophasal, ie, have the same scattering phase $s(ł)$ for all $ł> 0$. This is a scattering-theoretic analogue of isospectral domains. Using the heat invariants and the determinant of the Laplacian, Osgood, Phillips and Sarnak showed that each isospectral class is sequentially compact in
Hassell, Andrew, Zelditch, Steve
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