New Trends in Function Spaces and Partial Differential Equations: Theory and Applications to Physical Processes

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: closed (31 May 2021) | Viewed by 4325

Special Issue Editors

Faculty of Engineering and Architecture, University of Enna “KORE”, 94100 Enna, Italy
Interests: differential equation; symmetries; conservation laws
Dipartimento di Matematica e Informatica, Università degli Studi di Catania, Viale Andrea Doria 6, 95125 Catania, Italy
Interests: partial differential equations (regularity and existence theory, qualitative properties of the solutions); function spaces (e.g. Morrey-type spaces, function spaces with variable exponents, generalized function spaces, anisotropic function spaces) and their applications; integral operators; variational methods; nonlinear regularity theory; critical point theory; Morse theory and critical groups; mathematical modeling; ordinary differential equations and partial differential equations in the Applied Sciences (Physics, Biology, Ecology, Environmental Sciences, Engineering)

Special Issue Information

Dear Colleagues,

The aim of this Special Issue is to collect and announce the recent trends and improvements in the theory of function spaces and partial differential equations.

In the last decades a lot of studies concerning various function spaces are made. For instance, many authors studied Morrey-type spaces (e.g. generalized, weighted, vanishing, mixed Morrey spaces), Lebesgue, Hardy, Herz and Morrey spaces with variable exponents. It is worth pointing out that the idea of considering variable exponents is suggested by some studies related to the dynamic of electrorheological fluids. This way, the theory of function spaces, beside the proper purposes of the real analysis, moves towards physical applications. On the other hand, the theoretical investigation on the embeddings between function spaces and the boundedness of integral operators on them are of independent interest and attract a lot of researchers.

Moreover, several results regarding function spaces (e.g. boundedness of integral operators) are useful in the study of regularity properties to solutions of differential problems that arise from the Applied Sciences.

For the above reasons, papers dealing with issues in the contexts of both standard and non-standard function spaces with possible applications to partial differential equations are welcome.

This Special Issue also covers studies on deterministic and stochastic partial differential equations that describe physical and biological processes. In view of this wide spectrum of topics, papers that deal with theoretical aspects as regularity, existence, uniqueness as well as both analytic and numerical methods for the analysis of solutions will be considered. Moreover, the Special Issue will cover a wide range of mathematical problems in modern applied sciences with particular regards to classical and continuum models from an impressive array of disciplines, including: mathematical physics, biology, engineering problems, fluid and solid mechanics, physics and computer science. Mathematicians, physicists, engineers and other scientists whose research topics are close to differential equations are encouraged to submit their research to this Special Issue.


Topics for this Special Issue include, but are not limited to:

  • Function spaces,
  • Boundedness of integral operators on function spaces,
  • Regularity properties of solutions to partial differential equations in function spaces,
  • Existence and uniqueness of solutions to differential problems,
  • Partial differential equations in the Applied Sciences,
  • Mathematical models in Natural Sciences: environmental pollution, climate changes, desertification and related areas,
  • Mathematical models in quantum field theory,
  • Exact solutions to linear and nonlinear partial differential equations,
  • Fractional models and fractional calculus,
  • Asymptotic analysis and methods.

Prof. Ruggieri Marianna
Dr. Andrea Scapellato
Guest Editors

Published Papers (2 papers)

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Research

16 pages, 294 KiB  
Article
Boundedness of a Class of Oscillatory Singular Integral Operators and Their Commutators with Rough Kernel on Weighted Central Morrey Spaces
by Yongliang Zhou, Dunyan Yan and Mingquan Wei
Mathematics 2020, 8(9), 1455; https://doi.org/10.3390/math8091455 - 30 Aug 2020
Cited by 1 | Viewed by 1623
Abstract
In this paper, we establish the boundedness of a class of oscillatory singular integral operators with rough kernel on central Morrey spaces. Moreover, the boundedness for each of their commutators on weighted central Morrey spaces was also obtained. We generalized some existing results. [...] Read more.
In this paper, we establish the boundedness of a class of oscillatory singular integral operators with rough kernel on central Morrey spaces. Moreover, the boundedness for each of their commutators on weighted central Morrey spaces was also obtained. We generalized some existing results. Full article
11 pages, 256 KiB  
Article
An Improved Criterion for the Oscillation of Fourth-Order Differential Equations
by Omar Bazighifan, Marianna Ruggieri and Andrea Scapellato
Mathematics 2020, 8(4), 610; https://doi.org/10.3390/math8040610 - 16 Apr 2020
Cited by 33 | Viewed by 2015
Abstract
The main purpose of this manuscript is to show asymptotic properties of a class of differential equations with variable coefficients [...] Read more.
The main purpose of this manuscript is to show asymptotic properties of a class of differential equations with variable coefficients r ν w ν β + i = 1 j q i ν y κ g i ν = 0 , where ν ν 0 and w ν : = y ν + p ν y σ ν . By using integral averaging technique, we get conditions to ensure oscillation of solutions of this equation. The obtained results improve and generalize the earlier ones; finally an example is given to illustrate the criteria. Full article
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