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Showing 1 to 6 of 6 for “"Divergence Form"”.
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Obstacle problems with elliptic operators in divergence form
… obstacle problem with an elliptic operator in divergence form. First, I give all of the nontrivial details needed to prove a mean value theorem, which was stated by Caffarelli in the Fermi lectures in 1998. In fact, in 1963, Littman, Stampacchia, and Weinberger proved a mean value theorem for …
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Degenerate elliptic second-order differential operators with bounded complex-valued coefficients
… elliptic second-order differential operators in divergence form with bounded complex-valued coefficients. The main contribution of the thesis is in two parts. In one dimension we characterise when the space of test functions is a core for these operators. In higher dimensions we provide …
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Topics in harmonic analysis and partial differential equations: extension theorems and geometric maximum principles
… Lyapunov domain if and only if it satisfies a uniform hour-glass condition. The latter is a property of a purely geometrical nature, which amounts to the ability of threading the boundary, at any location, in between the two rounded components of a certain fixed region, whose shape resembles that …
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Homogenization of Random Media: Random Walks, Diffusions and Stochastic Interface Models
… is strictly convex with second derivative uniformly bounded below. The aforementioned annealed local limit theorem for the dynamic RCM is applied via a coupling relation to prove a scaling limit result for the space-time covariances in the Ginzburg-Landau model. We also show that the …
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Asymptotic theory for Bayesian nonparametric inference in statistical models arising from partial differential equations
… include a collection of parameters in their formulation, which are often unknown in applications and need to be estimated from the data. In the present thesis, we investigate the theoretical performance of nonparametric Bayesian procedures in such parameter identification problems in PDEs. In …
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Analytical Solutions of the SABR Stochastic Volatility Model
… one from obtaining a strictly speaking closed form solution of its joint transition density, namely the nonlinearity from the CEV type local volatility function, the coupling between the underlying asset process and the volatility process, and finally the correlation between the two driving …