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Boundary value problems in edge representationXiaochun, Liu, Schulze, Bert-Wolfgang January 2004 (has links)
Edge representations of operators on closed manifolds are known to induce large classes of operators that are elliptic on specific manifolds with edges, cf. [9]. We apply this idea to the case of boundary value problems. We establish a correspondence between standard ellipticity and ellipticity with respect to the principal symbolic hierarchy of the edge algebra of boundary value problems, where an embedded submanifold on the boundary plays the role of an edge. We first consider the case that the weight is equal to the smoothness and calculate the dimensions of kernels and cokernels of the associated principal edge symbols. Then we pass to elliptic edge operators for arbitrary weights and construct the additional edge conditions by applying relative index results for conormal symbols.
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Edge quantisation of elliptic operatorsDines, Nicoleta, Liu, X., Schulze, Bert-Wolfgang January 2004 (has links)
The ellipticity of operators on a manifold with edge is defined as the bijectivity of the components of a principal symbolic hierarchy σ = (σψ, σ∧), where the second component takes value in operators on the infinite model cone of the local wedges. In general understanding of edge problems there are two basic aspects: Quantisation of edge-degenerate operators in weighted Sobolev spaces, and verifying the elliptcity of the principal edge symbol σ∧ which includes the (in general not explicitly known) number of additional conditions on the edge of trace and potential type. We focus here on these queations and give explicit answers for a wide class of elliptic operators that are connected with the ellipticity of edge boundary value problems and reductions to the boundary. In particular, we study the edge quantisation and ellipticity for Dirichlet-Neumann operators with respect to interfaces of some codimension on a boundary. We show analogues of the Agranovich-Dynin formula for edge boundary value problems, and we establish relations of elliptic operators for different weights, via the spectral flow of the underlying conormal symbols.
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Conformal reduction of boundary problems for harmonic functions in a plane domain with strong singularities on the boundaryGrudsky, Serguey, Tarkhanov, Nikolai January 2012 (has links)
We consider the Dirichlet, Neumann and Zaremba problems for harmonic functions in a bounded plane domain with nonsmooth boundary. The boundary curve belongs to one of the following three classes: sectorial curves, logarithmic spirals and spirals of power type. To study the problem we apply a familiar method of Vekua-Muskhelishvili which consists in using a conformal mapping of the unit disk onto the domain to pull back the problem to a boundary problem for harmonic functions in the disk. This latter is reduced in turn to a Toeplitz operator equation on the unit circle with symbol bearing discontinuities of second kind. We develop a constructive invertibility theory for Toeplitz operators and thus derive solvability conditions as well as explicit formulas for solutions.
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Solving boundary value problems using critical point theoryFeller, Heidi. January 1900 (has links)
Thesis (Ph.D.)--University of Nebraska-Lincoln, 2008. / Title from title screen (site viewed Sept. 16, 2008). PDF text: vi, 91 p. : ill. ; 1 Mb. UMI publication number: AAT 3297751. Includes bibliographical references. Also available in microfilm and microfiche formats.
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Über das Neumann-Poincarésche Problem für ein Gebiet mit EckenCarleman, Torsten, January 1916 (has links)
Thesis (doctoral)--Uppsala universitet, 1917. / Includes bibliographical references.
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Zum Randwertproblem der partiellen Differentialgleichung der MinimalflächenMüntz, Chaim, January 1910 (has links)
Thesis (doctoral)--Friedrich-Wilhelms-Universität zu Berlin, 1910. / Published also as: Journal für die reine und angewandte Mathematik, Bd. 139, Heft 1. Vita.
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Local elliptic boundary value problems for the dirac operatorScholl, Matthew Gregory 28 August 2008 (has links)
Not available / text
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Fully automatic hp-adaptivity for acoustic and electromagnetic scattering in three dimensionsKurtz, Jason Patrick, 1979- 28 August 2008 (has links)
We present an algorithm for fully automatic hp-adaptivity for finite element approximations of elliptic and Maxwell boundary value problems in three dimensions. The algorithm automatically generates a sequence of coarse grids, and a corresponding sequence of fine grids, such that the energy norm of error decreases exponentially with respect to the number of degrees of freedom in either sequence. At each step, we employ a discrete optimization algorithm to determine the refinements for the current coarse grid such that the projection-based interpolation error for the current fine grid solution decreases with an optimal rate with respect to the number of degrees of freedom added by the refinement. The refinements are restricted only by the requirement that the resulting mesh is at most 1-irregular, but they may be anisotropic in both element size h and order of approximation p. While we cannot prove that our method converges at all, we present numerical evidence of exponential convergence for a diverse suite of model problems from acoustic and electromagnetic scattering. In particular we show that our method is well suited to the automatic resolution of exterior problems truncated by the introduction of a perfectly matched layer. To enable and accelerate the solution of these problems on commodity hardware, we include a detailed account of three critical aspects of our implementations, namely an efficient implementations of sum factorization, several interfaces to the direct multi-frontal solver MUMPS, and some fast direct solvers for the computation of a sequence of nested projections. / text
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EXISTENCE AND UNIQUENESS OF A TWO DIMENSIONAL FREE STREAMLINE GRAVITY FLOW FOR A LIQUID ISSUING FROM A CONTAINERSuitt, Clifton Bruce, 1942- January 1971 (has links)
No description available.
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Boundary value problems for linear elliptic PDEsSpence, Euan Alastair January 2011 (has links)
No description available.
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