Work

Composition and Products in Vector-valued Sobolev Spaces and Application

Year: 2024

Type: article

Abstract: In this paper, we will show the properties of composition operators $$u\rightarrow f\left(u\right)$$ in framework of $$E$$ -valued Sobolev and Lizorkin–Triebel spaces. Here $$E$$ is a Banach space. Boundedness and continuity properties will be discussed in a certain detail in Sobolev–Lions type function space concerning two abstract spaces $$E_{0}$$ and $$E$$ in terms of their interpolation. By using these composition properties, we obtain the local and global existence, uniqueness, and $$L^{p}$$ -regularity of some nonlinear abstract diffusion equations.

Source: Lobachevskii Journal of Mathematics

DOI: 10.1134/s1995080224600523

Author: V. B. Shakhmurov

Institutions: Western Caspian University, Azerbaijan State University of Economics, Antalya Bilim Üniversitesi, Antalya Bilim University

Language: English

Topic: Advanced Banach Space Theory

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4408515955

FWCI:

Cites: 11

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Related to: 10