The study of certain differential operators between Sobolev spaces of sections of vector bundles on compact manifolds equipped with rough metric is closely related to the study of locally Sobolev functions on domains in the Euclidean space. In this paper, we present a coherent rigorous s...
How can we fit the analytic concept of "differential operators" and "pseudo-differential operators" into the function analytic framework of "Hilbert space theory" (see Part I)? There is first of all the L 2 - concept of a Lebesgue measurable square integrable function which can be transferred...
For f∈Lp, the integral exists as an ordinary Lebesgue integral when p=1 while for p∈(1,2] it is defined by a limiting process; see [10, Sections 5.2.1–5.2.2]. For σ>0, let Bσ2 be the Bernstein space or Paley–Wiener space comprising all functions f∈L2, the Fourier transf...
Block-Sobolev space Sharp Mathematics Subject Classification 42B15 41A35 Access this article Log in via an institution Subscribe and save Springer+ Basic €32.70 /Month Get 10 units per month Download Article/Chapter or eBook 1 Unit = 1 Article or 1 Chapter Cancel anytime Subscribe now Buy...
Tomioka, Zakharov system in two space dimensions. Nonlinear Anal. 214, Paper No. 112532, 20 pp(2022). T. Ozawa, K. Tomioka, Global strong solutions of the coupled Klein-Gordon-Schrödinger equations. Funkcialaj Ekvacioj, 67, 229–265(2024). Article Google Scholar D. Chiron, F. ...
Moreover, the profile decomposition leads to results of decomposition of integral functionals of subcritical order. It is noteworthy that the space where the decomposition of integral functionals holds is the same as that where the residual term is vanishing....
We callqthe Coulomb–Sobolev exponent, and the spaceX1,αis continuously embedded inLsif and only ifsbelongs to the intervals in (1.3). Moreover, the best constantC>0of (1.2) is helpful to estimate the lower bound of the Coulomb energy [3,4]). The best constant of inequality (1.2) ...
Further sections describe the conformal invariance properties of Sobolev inequalities, and, as a consequence, the sharp Sobolev inequalities in the Euclidean and hyperbolic spaces on the basis of the one on the sphere, Gagliardo–Nirenberg inequalities and non-linear porous medium and fast diffusion ...
This paper consists of two sections excluding this introduction. Trace theorems for Sobolev-Slobodeckij spaces with and without weights are proved in section 2 and 3 respectively. Throughout the paper, we use the following notations. R d is a d-dimensional Euclidean space and (x 1 , x ) ...
To study (0.1)-(0.2), we first describe a family of general fractional Sobolev-Slobodeckij spaces Ms;q,p(ℝn) as well as their associated compact embedding results. Keywords: Sobolev-Slobodeckij spaces; compact embedding; fractional Laplacian; positive solutions MSC 2010: Primary 46E35; 35...