Search for dissertations about: "discrete Laplace operator"
Found 4 swedish dissertations containing the words discrete Laplace operator.
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1. Harmonic measures
Abstract : This thesis uses both analytic and probabilistic methods to study continuous and discrete problems. The main areas of study are the asymptotic properties of p-harmonic measure, and various aspects of the square root of the Poisson kernel. Fix a domain and a boundary point, subject to certain regularity conditions. READ MORE
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2. Combinatorial and analytical problems for fractals and their graph approximations
Abstract : The recent field of analysis on fractals has been studied under a probabilistic and analytic point of view. In this present work, we will focus on the analytic part developed by Kigami. The fractals we will be studying are finitely ramified self-similar sets, with emphasis on the post-critically finite ones. READ MORE
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3. Hardy-Lieb-Thirring inequalities for eigenvalues of Schrödinger operators
Abstract : This thesis is devoted to quantitative questions about the discrete spectrum of Schrödinger-type operators. In Paper I we show that the Lieb-Thirring inequalities on moments of negative eigen¬values remain true, with possibly different constants, when the critical Hardy weight is subtracted from the Laplace operator. READ MORE
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4. Properties of wave-front sets and non-tangential convergence
Abstract : In this thesis we consider regularity properties for solutions to partial differential equations and pseudo-differential equations. The thesis mainly concerns wave-front sets and micro-local properties. READ MORE