Reflections on Dubinskiĭ’s Nonlinear Compact Embedding Theorem
نویسندگان
چکیده
We present an overview of a result by Yulĭı Andreevich Dubinskĭı [Mat. Sb. 67 (109) (1965); translated in Amer. Math. Soc. Transl. (2) 67 (1968)], concerning the compact embedding of a seminormed set in L(0, T ;A0), where A0 is a Banach space and p ∈ [1, ∞]; we establish a variant of Dubinskĭı’s theorem, where a seminormed nonnegative cone is used instead of a seminormed set; and we explore the connections of these results with a nonlinear compact embedding theorem due to Emmanuel Maitre [Int. J. Math. Math. Sci. 27 (2003)].
منابع مشابه
Embedding normed linear spaces into $C(X)$
It is well known that every (real or complex) normed linear space $L$ is isometrically embeddable into $C(X)$ for some compact Hausdorff space $X$. Here $X$ is the closed unit ball of $L^*$ (the set of all continuous scalar-valued linear mappings on $L$) endowed with the weak$^*$ topology, which is compact by the Banach--Alaoglu theorem. We prove that the compact Hausdorff space $X$ can ...
متن کاملA Hardy Inequality with Remainder Terms in the Heisenberg Group and the Weighted Eigenvalue Problem
Based on properties of vector fields, we prove Hardy inequalities with remainder terms in the Heisenberg group and a compact embedding in weighted Sobolev spaces. The best constants in Hardy inequalities are determined. Then we discuss the existence of solutions for the nonlinear eigenvalue problems in the Heisenberg group with weights for the psub-Laplacian. The asymptotic behaviour, simplicit...
متن کاملEmbeddability of Some Strongly Pseudoconvex Cr Manifolds
We obtain an embedding theorem for compact strongly pseudoconvex CR manifolds which are bounadries of some complete Hermitian manifolds. We use this to compactify some negatively curved Kähler manifolds with compact strongly pseudoconvex boundary. An embedding theorem for Sasakian manifolds is also derived.
متن کاملFixed point theorem for non-self mappings and its applications in the modular space
In this paper, based on [A. Razani, V. Rako$check{c}$evi$acute{c}$ and Z. Goodarzi, Nonself mappings in modular spaces and common fixed point theorems, Cent. Eur. J. Math. 2 (2010) 357-366.] a fixed point theorem for non-self contraction mapping $T$ in the modular space $X_rho$ is presented. Moreover, we study a new version of Krasnoseleskii's fixed point theorem for $S+T$, where $T$ is a cont...
متن کاملPositive solutions for P-Laplace problems with nonlinear time-fractional differential equation
In this paper, we study the existence and multiplicity of positive solutions for semi-linear elliptic equations with a sign-changing weight function in weighted Sobolev spaces. By investigating the compact embedding theorem and based on the extraction of the Palais-Smale sequence in the Nehari manifold which is a subset of the weighted Sobolev spaces, we derive the existence of the multiple pos...
متن کامل