Work

Sharp Lp -Regular Nonlocal Differential Operators and Applications

Year: 2025

Type: article

Abstract: The maximal regularity properties of a fractional anisotropic elliptic equation are investigated. The equation involves an abstract linear operator $$A$$ A in Fourier type Banach space $$E$$ E and convolution terms. We find the sufficient conditions that guarantee the separability of this problems in $$E$$ E -valued weighted $${L}_{p}$$ L p spaces. We prove that an anisotropic elliptic operator generated by this problem is sectorial and generates an analytic semigroup. In application, the maximal regularity properties of the Cauchy problem for degenerate abstract anisotropic parabolic equation and the boundary value problem for anisotropic elliptic convolution equation are obtained in mixed $${L}_{\mathbf{p}}$$ L p norms.

Source: Complex Analysis and Operator Theory

DOI: 10.1007/s11785-025-01663-0

Authors: Veli B. Shakhmurov, Rishad Shahmurov

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

Language: English

Topic: Differential Equations and Boundary Problems

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

OpenAlex ID: W4407871242

FWCI: 1.876

Cites: 28

Cited by: 1

Related to: 10