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Showing 1 to 20 of 109 for “"Sobolev"”.
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Noncommutative Sobolev type inequalities
In this thesis, we study Sobolev type inequalities in the noncommutative (quantum) settings. We establish the abstract Bakry-\'Emery criterion for the operator-valued $f$-Sobolev inequalities on the derivation triple. We recapture the celebrated Bakry-\'Emery theorem for operator-valued functions …
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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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Sobolev tests for uniformity on compact Riemannian manifolds,
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 1973
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Identifying Optimal Mixing Strategies and Structures through Sobolev Norms
… flows. These multiscale measures, equivalent to Sobolev norms of negative index, have been employed successfully for this purpose. This thesis investigates these norms and their use in nonlinear optimal mixing problems. In Chapter 3, we compare the optimisation of the classical variance measure …
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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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Applied left-definite theory : the Jacobi polynomials, their Sobolev orthogonality, and self-adjoint operators.
… known that they are orthogonal with respect to a Sobolev inner product. In this work, we first consider the special case where α = β = –1. We shall discuss the Sobolev orthogonality of the Jacobi polynomials and construct a self-adjoint operator in a certain Hilbert-Sobolev space having the entire …
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Probability measure estimation in positron emission tomography using loss functions based on Sobolev norms
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1994.
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Bounds on the growth of high Sobolev norms of solutions to nonlinear Schrödinger equations
In this thesis, we study the growth of Sobolev norms of global solutions of solutions to nonlinear Schrödinger type equations which we can't bound from above by energy conservation. The growth of such norms gives a quantitative estimate on the low-to high frequency cascade which can occur due to …
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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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Nodal geometry of eigenfunctions on smooth manifolds and hardy-littlewood-sobolev inequalities on the heisenberg group
… dimension Q=2n+2, we study the Hardy-Littlewood-Sobolev (HLS) inequality,</p> <p>and particularly its sharp version. Weighted Hardy-Littlewood-Sobolev inequalities with different weights shall also be investigated, and we solve the following problems.</p> <p>(1) Establish the existence results of …
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Global in time existence of Sobolev solutions to semi-linear damped sigma-evolution equations in L^q scales
… the global (in time) existence of small data Sobolev solutions to semi-linear damped σ-evolution equations from suitable function spaces basing on L^q spaces by mixing additional L^m regularity for the data on the basis of L^q-L^q estimates for solutions, with q∈(1,∞) and m∈[1,q), to the …
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Smoothing estimates for non commutative spaces
… perspective to establish the noncommutaive Sobolev inequaties (namely, Hardy-Littlewood-Sobolev inequalites), and extend the Sobolev embedding from noncommutative $L_p$ spaces to general Orlicz function spaces related with Cowling and Meda's work. Also we will show some examples to …
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Basic functional and geometric inequalities for the fractional order operators on homogenous Lie groups
… direct inequalities we obtain fractional Hardy, Sobolev, Hardy-Sobolev, Gagliardo-Nirenberg, Caffarelli-Kohn-Nirenberg, logarithmic inequal- ities, Hardy-Littlewood-Sobolev and Stein-Weiss inequalities on homogeneous Lie groups. Also, we obtain the integer order Sobolev-Folland-Stein inequality …
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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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Laplacians on Nonisotropic Heisenberg Groups with Multi-Dimensional Center
… 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 transforms and the Lp Lq estimates of these heat semigroups are presented. Finally, the eigenvalues …
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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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Teoremas de inmersión
… En primer lugar se estudian inmersiones tipo Sobolev para espacios anisótropos; esto es inmersiones óptimas de espacios de Sobolev en espacios de Lorentz y en espacios de Besov. Se abarca también el caso más complejo en el que algunos índices p son iguales a 1. También se estudian inmersiones …
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