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Showing 1 to 15 of 15 for “"Sobolev Space"”.
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Development of potential-based time domain integral equations for quantum electrodynamics modeling
… functional framework is utilized to analyze the Sobolev space properties of these integral equations. Discretizations formulated to conform to these Sobolev space properties are shown to be substantially more stable numerically than traditional discretization approaches. These new computational …
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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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Theoretical and computational studies in seismic tomography
… an approach for determining a suitable function space to use as a model space in geophysical inverse problems, including seismic tomography. In particular, we show that a Sobolev space is often a suitable choice, and allows us to specify a required degree of regularity for model parameters. We …
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Stochastic hypodissipative hydrodynamic equations: well-posedness, stationary solutions and ergodicity
… the system with initial data in the anisotropic Sobolev space \tilde {H}<sup>*0,1*</sup>. For the stochastic case, we obtain the existence of martingale solutions and pathwise uniqueness of the solutions, which imply the existence of the probabilistically strong solution to this system by the …
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Finite element methods for parameter identification problem of linear and nonlinear steady-state diffusion equations
… in the cost functional in an appropriate Sobolev space. The existence and uniqueness of the minimizer for the cost functional is proved. Error estimates in a weighted 𝐻⁻¹-norm, 𝐿²-norm and 𝐿¹-norm for the numerical solution are derived. Numerical examples will be given to show features of …
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Supercritical Semi-Linear Elliptic Problems Using Variational Principles
… By focusing on convex subsets of a Banach space, the research overcomes compactness issues typically encountered with nonlinearities that exceed the Sobolev embedding exponent. This enables the effective use of standard variational techniques, leading to existence results for solutions. The …
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Monotone and pseudomonotone operators with applications to variational problems
… and pseudomonotone operators between Banach spaces are used to prove the existence of solutions to nonlinear elliptic boundary value problems. A well-known approach to solving nonlinear elliptic boundary value problems is to reformulate them as equations of the form A (u) = f, where A is a …
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Generalisations of Pick's theorem to reproducing Kernel Hilbert spaces
… only if a certain matrix is positive. H1 is the space of multipliers of H2 and this theorem has a natural generalisation when H1 is replaced by the space of multipliers of a general reproducing kernel Hilbert space H(K) (where K is the reproducing kernel). J. Agler showed that this generalised …
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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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Continuity Properties and Variational Problems Involving the Determinant of the Hessian
… of a scalar function u in various function spaces. It is well known that when D is a bounded, open subset of n-dimensional Euclidean space Rn, the distributional determinant of the Hessian is weakly continuous in the Sobolev space of functions whose second derivatives are Lp functions on D, …
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Articles on Potential Theory, Functional Analysis and Hankel Forms
… the Neumann-Poincaré operator, is studied on the Sobolev space of order $1/2$ along the boundary, coinciding with the space of charges giving rise to double layer potentials with finite energy in the whole space. Poincaré's program of studying the spectrum of the boundary double layer potential is …
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Regularity of the D-bar-Neumann Operator, the Bergman Projection and the Canonical Solution Operator of D-bar-Equation
… Bergman projection on the weighted $L^p$ spaces on the unit disk. As a consequence, we obtain the boundedness of the Bergman projection on weighted Sobolev space on the symmetrized bidisk. We also improve previous results on the boundedness of the Bergman projection on unweighted $L^p$ …
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Convergence of Kernel Methods for Modeling and Estimation of Dynamical Systems
… modeling methods, the reproducing kernel Hilbert space (RKHS) embedding method and the empirical-analytical Lagrangian (EAL) model. RKHS embedding is a non-parametric extension of the classical adaptive estimation method that embeds the uncertain function in an RKHS, an infinite-dimensional …
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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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TWO RESULTS ON THE GLOBAL DYNAMICS OF PDES ON THE CIRCLE.
… of the Klein-Gordon equation in H^s, the Sobolev space of s-regularity, with s large enough. This family, uniformly in time, remains close to the corresponding quasi-periodic solutions family of the cubic nonlinear Schrödinger, which are still defined in H^s. More precisely, we prove that …