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Showing 1 to 20 of 26 for “"Elliptic Equations"”.
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CLASSIFICATION RESULTS FOR SEMILINEAR ELLIPTIC EQUATIONS
… problems of solutions to semilinear elliptic equations, with a particular focus on the study of symmetry and rigidity results. The thesis is divided into four chapters. In Chapter 1 we consider solutions to some semilinear elliptic equations on complete noncompact Riemannian manifolds …
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A SYSTEM OF SUPERLINEAR ELLIPTIC EQUATIONS IN A CYLINDER
… of existence of positive solutions of nonlinear elliptic boundary value problems. An important way to deal with the problem is the study of a priori estimates of positive solutions. We will adapt a classical idea which was introduced by Brezis and Turner and, together with a fixed point theorem, …
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Symmetry properties of semilinear elliptic equations with isolated singularities
… properties for positive solutions of semilinear elliptic equations. We give a detailed proof of the result due to Caffarelli, Gidas, and Spruck that a solution in the punctured ball, B\{0}, behaves asymptotically like its spherical average at the origin. We also show that a solution with an …
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Blowing-up patterns in semilinear elliptic equations of critical type
Hay dos partes en mi tesis. La primera parte se dedica principalmente a la construcción de soluciones burbujeantes de algunos problemas elípticos con no linealidad exponencial en $\mathbb{R}^2$. En la segunda parte se considera la existencia de soluciones de punta para ecuaciones elípticas en …
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Existence of Solutions Via a New Variational Principle for Nonlocal Semilinear Elliptic Equations
… of a weak solution for semilinear fractional elliptic equations given by \begin{eqnarray*}\left\{ \begin{array}{ll} (-\Delta)^s u=|u|^{p-2} u+ f(x),& \quad x\in \Omega,\\ u=0, & \quad x \in \R^n \backslash \Omega, %0, & \quad x \in \partial \Oemga, \end{array} \right. \end{eqnarray*} where …
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Error estimates for finite difference solutions of second-order elliptic equations in discrete Sobolev spaces
… for nite difference solutions of second-order elliptic equations with continuous coefficients in the whole space. We shall mainly use the Fefferman-Stein theorem and discrete Sobolev inequalities to establish our purpose. Based on these lp-estimates, we obtain the convergence rate of the …
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Numerical analysis of the Fokas method in two and three dimensions
This thesis considers the numerical solution to elliptic boundary value problems (BVPs) in convex domains. Specifically we look at the two-dimensional problem in a polygon, and the three dimensional problem in a polyhedron. The nature of elliptic equations means that, knowing the values of a …
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Qualitative Properties Of Solutions Of Fully Nonlinear Equations And Overdetermined Problems
… of fully nonlinear partial differential equations. We</p> <p>obtain the radial symmetry and monotonicity properties for</p> <p>nonnegative viscosity solutions of fully nonlinear equations under some asymptotic decay rate at infinity. Our symmetry and monotonicity results also</p> <p>apply …
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Moser-Trudinger And Adams Type Inequalities And Their Applications
… results, we also study in this dissertation the elliptic equations that contain the exponential nonlinearities.</p>
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Regularity results for some elliptic and parabolic problems
… of solutions to nonlinear partial differential equations of elliptic and parabolic type, and it collects some results obtained during the last three years under the supervision of Prof. Ugo Gianazza The first part concernes the study of singular porous medium type equations: we start proving …
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Global a priori Estimates and Sharp Existence Results for Quasilinear Equations on Nonsmooth Domains.
… global a priori estimates for quasilinear elliptic equations and sharp existence results for Quasilinear equations with gradient nonlinearity on the right. The main results are contained in Chapters 3, 4, 5 and 6. In Chapters 3 and 4, we obtain global unweighted a priori estimates for very …
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Semilinear elliptic partial differential equations with the critical Sobolev exponent
… applied to solving certain types of semilinear elliptic partial differential equations (PDEs). The ultimate goal is to prove results on the existence and non-existence of solutions to the Semilinear Elliptic PDEs with the Critical Sobolev Exponent. To this end, we first recall some useful …
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A general inverse design procedure for aerodynamic bodies
… of the procedure to solve problems governed by elliptic equations. A 3-D, viscous, compressible flow over a forebody/canopy model of a supersonic fighter and its comparison to test data establishes the ability of the method to solve practical problems of interest. Several other test cases are …
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Regularity theory for nonlocal equations
… of Calderón-Zygmund-type for nonlinear nonlocal equations with possibly very irregular coefficients of VMO-type or even coefficients that are merely small in BMO. In particular, such coefficients might be discontinuous.<br /><br />While for corresponding local elliptic equations with VMO …
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Critical perturbations of elliptic operators by lower order terms
… solutions of certain boundary value problems for elliptic equations in the upper half-space. More specifically we treat the Dirichlet, Neumann, and Regularity problems for the general second order, linear, elliptic operator under a smallness assumption on the coefficients in certain critical …
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Nonlinear Methods in the Study of Singular Partial Differential Equations
Nonlinear singular partial differential equations arise naturally when studying models from such areas as Riemannian geometry, applied probability, mathematical physics and biology. The purpose of this thesis is to develop analytical methods to investigate a large class of nonlinear elliptic PDEs …
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ANALYZING AND IMPROVING INITIAL DATA FOR BINARY BLACK HOLES
… fully numerical methods for solving Einstein's equations. Numerical simulations of binary black holes require the specification of initial data to be used with evolution equations. The physics of a binary black hole system in numerical relativity will largely be determined by the initial data. …
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Design, Analysis, and Application of Immersed Finite Element Methods
… face problems related to partial differential equations (PDEs) with discontinuous coefficients. These three topics together form a continuation of the research in IFE method including the extension to elasticity systems, new breakthroughs to higher degree IFE methods, and its application to …
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Initial and boundary value problems in two and three dimensions
… 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 operator in the interior of an …
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