Results 41 to 50 of about 211 (144)

Generalized versus classical normal derivative [PDF]

, 2023
Given a bounded domain with Lipschitz boundary, the general Green formula permits to justify that the weak solutions of a Neumann elliptic problem satisfy the Neumann boundary condition in a weak sense.
MOTREANU, Viorica V., Viorica V. Motreanu, FRESSE, Lucas, Lucas Fresse   +3 more
core   +1 more source

Characterization of Riesz and Bessel potentials on variable Lebesgue spaces

Journal of Function Spaces, Volume 4, Issue 2, Page 113-144, 2006., 2006
Riesz and Bessel potential spaces are studied within the framework of the Lebesgue spaces with variable exponent. It is shown that the spaces of these potentials can be characterized in terms of convergence of hypersingular integrals, if one assumes that the exponent satisfies natural regularity conditions. As a consequence of this characterization, we
Alexandre Almeida, Stefan Samko, Vakhtang Kokilashvili   +2 more
wiley   +1 more source

Weierstrass' theorem in weighted Sobolev spaces with k derivatives [PDF]

, 2007
36 pages, no figures.-- MSC2000 codes: 41A10, 46E35, 46G10.MR#: MR2382639 (2008m:41022)Zbl#: Zbl 1177.41007We characterize the set of functions which can be approximated by smooth functions and by polynomials with the norm $$ \ \ ^{(j)}\ {W^{k,\infty}_w}=
Tourís, Eva, Rodríguez, José M., Quintana, Yamilet, Portilla, Ana   +3 more
core   +2 more sources

Analyze Second‐Order PDEs Using the Volterra–Fredholm Integral Equation

Journal of Function Spaces, Volume 2025, Issue 1, 2025.
In this study, we propose a novel approach to address a particular second‐order partial differential equation along with its boundary value conditions (SPDEs). In this process, we transfer the SPDEs problem into Volterra–Fredholm integral equation (VFIE), and we perform the Tau method bases on orthogonal Legendre polynomials directly, for solution of ...
Choonkil Park, Javad Shokri, Richard I. Avery   +2 more
wiley   +1 more source

Sobolev type inequalities in ultrasymmetric spaces with applications to Orlicz‐Sobolev embeddings

Journal of Function Spaces, Volume 3, Issue 2, Page 183-208, 2005., 2005
Let Dkf mean the vector composed by all partial derivatives of order k of a function f(x), x ∈ Ω ⊂ ℝn. Given a Banach function space A, we look for a possibly small space B such that ‖f‖B≤c‖|Dkf|‖A for all f∈C0k(Ω). The estimates obtained are applied to ultrasymmetric spaces A = Lφ,E, B = Lψ,E, giving some optimal (or rather sharp) relations between ...
Evgeniy Pustylnik, Lech Maligranda
wiley   +1 more source

Domains of pseudo‐differential operators: a case for the Triebel‐Lizorkin spaces

Journal of Function Spaces, Volume 3, Issue 3, Page 263-286, 2005., 2005
The main result is that every pseudo‐differential operator of type 1, 1 and order d is continuous from the Triebel‐Lizorkin space Fp,1d to Lp, 1 ≤ p≺∞, and that this is optimal within the Besov and Triebel‐Lizorkin scales. The proof also leads to the known continuity for s≻d, while for all real s the sufficiency of Hörmander′s condition on the twisted ...
Jon Johnsen, Victor Burenkov
wiley   +1 more source

Approximation theory for weighted Sobolev spaces on curves [PDF]

, 2001
17 pages, no figures.-- MSC2000 codes: 41A10, 46E35, 46G10.MR#: MR1882649 (2003c:42002)In this paper we present a definition of weighted Sobolev spaces on curves and find general conditions under which the spaces are complete.
Pestana, Domingo, Romera, Elena, Álvarez, Venancio, Rodríguez, José M.   +3 more
core   +2 more sources

Sobolev extension in a simple case

Advanced Nonlinear Studies
In this paper, we establish the existence of a bounded, linear extension operator T:L2,p(E)→L2,p(R2) $T :{L}^{2,p}\left(E\right)\to {L}^{2,p}\left({\mathbb{R}}^{2}\right)$ when 1 < p < 2 and E is a finite subset of R2 ${\mathbb{R}}^{2}$ contained in a ...
Drake Marjorie, Fefferman Charles, Ren Kevin, Skorobogatova Anna   +3 more
doaj   +1 more source

Generalized homogeneous Besov spaces and their applications [PDF]

, 2012
2010 Mathematics Subject Classification: Primary 35L05. Secondary 46E35, 35J25, 22E30.In this paper we define the homogeneous Besov spaces associated with the Dunkl operators on R^d, and we give a complete analysis on these spaces and same ...
Mejjaoli, Hatem
core  

Logarithmic asymptotics of contracted Sobolev extremal polynomials on the real line [PDF]

, 2006
12 pages, no figures.-- MSC2000 codes: 41A60, 46E35.MR#: MR2271726 (2007h:41031)Zbl#: Zbl 1106.41031For a wide class of Sobolev type norms with respect to measures with unbounded support on the real line, the contracted zero distribution and the ...
Marcellán, Francisco, López Lagomasino, Guillermo, Pijeira, Héctor, Cabrera, H. Pijeira, Español, F. Marcellán, Marcellán Español, Francisco José, Lagomasino, G. López, Pijeira Cabrera, Héctor Esteban   +7 more
core   +1 more source