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Showing 1 to 13 of 13 for “"Laplace Operator"”.
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Eigenvalue Problem for the 1-Laplace Operator
… the eigenvalue problem associated to the 1-Laplace operator. We define higher eigensolutions by means of weak slope and establish existence of a sequence of eigensolutions by using nonsmooth critical point theory. In addition, we deduce a new necessary condition for the first eigenvalue of …
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On two problems related to the Laplace operator
We investigate maximization of the functional Ω → ε(Ω) where Ω runs in the set of compact domains of fixed volume v in any Riemannian manifold (M; g) and where ε(Ω) is the mean exit time from of the Brownian motion. Concerning this functional, we study its critical points and prove that they are …
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Unique continuation theorems for the Dirac operator and the Laplace operator
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1989.
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Asymptotic bounds and values for the norm of the Laplace operator and other partial differential operators on spaces of polynomials
… beschränkt. Wir betrachten auf diesen Räumen den Laplaceoperator und zwei weitere partielle Differentialoperatoren und interessieren uns für das Verhalten der von den Polynomnormen induzierten Operatornormen dieser Operatoren, wenn n gegen unendlich strebt. Im Fall der Laguerre- und Legendrenorm …
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Variational convergence of nonlinear partial differential operators on varying Banach spaces
… quasi-linearen monotonen partiellen Differenzialoperatoren erarbeitet. Zu diesem Zwecke wird die so genannte Kuwae-Shioya-Konvergenz von metrischen Räumen genauer im Banach-Raum-Fall untersucht. Erstmals werden schwache Banach-Raum-Topologien mit eingebunden. Wir erfüllen das Ziel, sinnvolle …
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Existence of Solutions Via a New Variational Principle for Nonlocal Semilinear Elliptic Equations
… where $(-\Delta)^s$ denotes the fractional Laplace operator with $s \in (0,1],$ $n > 2s,$ $\Omega$ is an open bounded domain in $\R^n$ with $C^2$-boundary and $f \in L^2(\Omega).$ We are interested in extending this result for $s \in (0, 1]$ to $p$ greater than the critical Sobolev exponent …
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Initial and boundary value problems in two and three dimensions
… several boundary value problems (BVPs) for the Laplace and the modified Helmholtz equations in the interior of an equilateral triangle; (b) presents the solution of the heat equation in the interior of an equilateral triangle; (c) computes the eigenvalues and eigenfunctions of the Laplace …
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Anti-self-dual fields and manifolds
… rise to a conformally invariant differential operator, special cases of the associated generalised Laplace operator are the conformal Laplacian and the linearised Przanowski operator. Using recursion relations we construct a contour integral formula for perturbations of Przanowski’s function. …
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Eine $L^q$-Theorie des Cosseratspektrums in beschränkten Gebieten und Außengebieten
… beruht auf der Theorie der Pseudodifferentialoperatoren. Faierman, Fries, Mennicken und Möller (2000) führten einen direkten Beweis für beschränkte Gebiete, n>=2 und q=2. Michel Crouzeix gelang 1997 ein sehr einfacher Beweis für beschränkte Gebiete, n=2,3 und q=2. In dieser Arbeit wird die …
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Multi-dimensional continuous wavelet transforms and generalized fourier transforms in Clifford analysis
… are null-solutions of the so-called Dirac operator, a first order rotationally invariant differential operator factorizing the Laplacian in higher dimensions. This factorization of the Laplace operator establishes a special relationship between monogenic functions and harmonic functions of …
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LAPLACIAN TYPE EQUATIONS
… non lineari in diversi spazi ambiente, con operatori p-Laplaciano e (p, q)-Laplaciano, dove p e q possono essere numeri reali o funzioni a valori reali. Si tratta di un importante campo di applicazione dei metodi variazionali, che sono utili strumenti non solo per studiare l'esistenza di …
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Local Factorization of Multidimensional Differential Operators to Optimize Implicit Solution Methods
Solving multidimensional differential operators using implicit finite-difference methods involves a computationally intensive step of calculating the solution to a system that involves both the current and future state of the system. If a linear operator can be expressed as an affine combination of …
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Semiclassical spectral analysis of discrete Witten Laplacians
… lattice is considered. After rescaling of the operator and the lattice size we analyze the tunnel effect between different wells, providing sharp asymptotics of the low-lying spectrum. Our proof, inspired by work of B. Helffer, M. Klein and F. Nier in continuous setting, is based on the …