نتایج جستجو برای: generalized lebesgue sobolev spaces
تعداد نتایج: 295657 فیلتر نتایج به سال:
In this paper, error estimates for generalized Laguerre–Gauss-type interpolations are derived in nonuniformly weighted Sobolev spaces weighted with ωα,β(x) = x αe−βx, α > −1, β > 0. Generalized Laguerre pseudospectral methods are analyzed and implemented. Two model problems are considered. The proposed schemes keep spectral accuracy and, with suitable choice of basis functions, lead to sparse a...
We give an intrinsic characterization of the restrictions of Sobolev W k p (R n), Triebel-Lizorkin F s pq (R n) and Besov B s pq (R n) spaces to regular subsets of R n via sharp maximal functions and local approximations. The purpose of this paper is to study the problem of extendability of functions defined on measurable subsets of R n to functions defined on the whole space and satisfying cer...
The incompressible limit of nonlinear diffusion equations porous medium type has attracted a lot attention in recent years, due to its ability link the weak formulation cell-population models free boundary problems Hele-Shaw type. Although vast literature is available on this singular limit, little known convergence rate solutions. In work, we compute negative Sobolev norm and, upon interpolati...
In this work we discuss the generalized treatment of the deformable registration problem in Sobolev spaces. We extend previous approaches in two points: 1) by employing a general energy model which includes a regularization term, and 2) by changing the notion of distance in the Sobolev space by problem-dependent Riemannian metrics. The actual choice of the metric is such that it has a precondit...
The classical Grüss and related inequalities have spurred a range of improvements, refinements, generalizations, extensions. In the present article, we provide generalizations Sokolov’s inequality in weighted Lebesgue LωΩ,A,μ spaces by employing Sonin’s identity Čebyšev functional. As result, generalized which bounding constants are improved with functions LωpΩ,A,μ spaces. an application, sever...
For d≥3, we prove that time-inhomogeneous stochastic differential equations driven by additive noises with drifts in critical Lebesgue space Lq([0,T];Lp(Rd)), where (p,q)∈(d,∞]×[2,∞) and d∕p+2∕q=1, or (p,q)=(d,∞) divb∈L∞([0,T];Ld∕2+ε(Rd)), are well-posed. The weak uniqueness is obtained solving corresponding Kolmogorov backward some second-order Sobolev spaces, which analytically interesting it...
We study bounded trace maps on hypersurfaces for Sobolev spaces from a point of view that is fundamentally different the one in classical theory. This allows us to construct under weak regularity assumptions hypersurfaces. In case domains $\mathbf R^n$ we only require continuity boundary. For whole space assume are Lebesgue measurable. As an application our consider Dirichlet problem and prove ...
hold. The facts above are well-known as the classical Shannon sampling theorem initially proved by Ogura [10]. Ashino and Mandai [1] generalized the sampling theorem in Lebesgue spaces L0(R) for 1 < p0 < ∞. Their generalized sampling theorem is the following. Theorem 1.1 ([1]). Let r > 0 and 1 < p0 < ∞. Then for all f ∈ L 0(R) with supp f̂ ⊂ [−rπ, rπ], we have the norm inequality C p r ‖f‖Lp0(Rn...
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