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Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 35 for “"Sobolev spaces."”.
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New Characterizations Of Sobolev Spaces On Heisenberg And Carnot Groups And High Order Sobolev Spaces On Eucliean Spaces
… dissertation focuses on new characterizations of Sobolev spaces .</p> <p>It encompasses an in-depth study of Sobolev spaces on Heisenberg groups, as well as Carnot groups, second order and high order Sobolev spaces on Euclidean spaces.</p>
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Restriction to hypersurfaces of non-isotropic Sobolev spaces
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1993.
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Error estimates for finite difference solutions of second-order elliptic equations in discrete Sobolev spaces
… 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 approximate solutions and their difference quotients in the sup norm.
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Laplacians on Nonisotropic Heisenberg Groups with Multi-Dimensional Center
… in the Schwartz space and in the Gelfand-Shilov spaces using the Green functions of the twisted Laplacians. Global regularity in a scale of Sobolev spaces of these twisted Laplacians is given. Equally important are the heat semigroups generated by the twisted Laplacians in terms of Weyl …
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Regularity of Solution Maps of the Generalized Surface Quasi-Geostrophic Equations
… equations fails to be uniformly continuous in Sobolev spaces.
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Sobre a teoria de regularidade elíptica via análise da equação de Helmholtz em RN
… Analysis, Functional Analysis and the Theory of Sobolev Spaces.
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Constructive approaches to quasi-Monte Carlo methods for multiple integration
… worst-case error bounds in weighted function spaces in which the importance of the variables is moderated by some sequences of weights. Ideally, a family of quasi-Monte Carlo methods in some weighted function space should be strongly tractable. Strong tractability means that the minimal number …
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Variational Methods for Nonlinear Partial Differential Equations
… the energy functional is defined over subsets of Sobolev spaces. After that, the technical concepts associated to this theorem are implemented to study some specific free boundary problems.
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The Fock-Schwartz spin representation space
In this thesis, we define and study a family of Sobolev-like subspaces (the “FockSobolev spaces”) and the corresponding Schwartz-like space (the “Fock-Schwartz space”) arising from the infinite-dimensional spin representation constructed by Pressley and Segal. In particular, we study the …
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Radiation field for Einstein vacuum equations
… small neighborhoods of suitable weighted b-type Sobolev spaces.
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A Gauge-Theoretic Approach to the Chern Form of the Canonical Bundle on the Moduli Space of Stable Parabolic Bundles
… on a closed Riemann surface using weighted Sobolev spaces. We study the metric properties of the moduli space, and in particular, we compute the L2 curvature of its canonical bundle. By identifying the canonical bundle with the index bundle of a suitable family of Dolbeault operators, we …
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Leibniz-type rules associated to bilinear pseudodifferential operators
… identically equal to one. A variety of function spaces may be used to measure the size and smoothness of functions involved, including Lebesgue spaces, Sobolev spaces, and Besov and Triebel-Lizorkin spaces. Further, bilinear pseudodifferential operators may be considered in association with …
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Semilinear elliptic partial differential equations with the critical Sobolev exponent
… the Semilinear Elliptic PDEs with the Critical Sobolev Exponent. To this end, we first recall some useful results from functional analysis, including the Sobolev spaces, which provide a natural setting for the idea of weak or generalised solutions. We then present linear PDE theory, including …
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Extension of the Hodge theorem to certain non-compact manifolds
… boundary ... We then describe doubly weighted Sobolev spaces on M. For elements of these spaces the harmonic parts of w1 and w2 lie in one Sobolev space, while the non-harmonic parts of w1 and w2 lie in a differently defined Sobolev space. We prove that ... is Fredholm on almost all of these …
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Global normal forms and global properties in function spaces for second order Shubin type operators
… type differential operators P(x;D) in functional spaces on Rn. We describe the isomorphism properties of normal form transformations, introduced by L. Hormander for the study of affine symplectic transformations acting on pseudodifferential operators, in spaces like the Schwartz class, the …
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Generalisations of Pick's theorem to reproducing Kernel Hilbert spaces
… theorem is true when H(K) is a certain Sobolev space or the Dirichlet space. This thesis widens Agler's approach to cover reproducing kernel Hilbert spaces in general and derives sucient (and usable) conditions on the kernel K, for the generalised Pick's theorem to be true for H(K). …
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The Beurling-Ahlfors extension and Conformal welding
… we begin by introducing the fundamentals of Sobolev spaces and present some theorems that allow us to study the properties of compositions of quasiconformal functions. We prove Stoilow's factorization theorem and use it to show that the solution to Beltrami's equation can naturally be …
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Sequences of compact curvature
… it depends on the structure of the underlying spaces whether or not an operator is "small." This leads to a magical mix of perturbation and regularisation theory. In the general setting of Hilbert spaces compact operators are "small." In order to develop this theory, many elements of diverse …
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Understanding and Improving Moment Method Scattering Solutions
… the moment method have been obtained in terms of Sobolev norms of the current solution. Motivated by the historical origins of Sobolev spaces as energy spaces, it is shown that the Sobolev norm used in these bounds is equivalent to the forward scattering amplitude, for the case of 2D scattering …
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Nonhomogeneous Initial Boundary Value Problems for Two-Dimensional Nonlinear Schrodinger Equations
… for the appropriate initial and boundary data in Sobolev spaces H^s with non-negative s and investigates the global well-posedness in the H^1-space. The main strategy, especially for the local well-posedness, is to derive an equivalent integral equation (whose solution is called mild solution) …
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