Results 21 to 30 of about 1,287 (117)

Parabolic equations in Musielak - Orlicz spaces with discontinuous in time N-function [PDF]

Journal of Differential Equations, 2021
We consider a parabolic PDE with Dirichlet boundary condition and monotone operator $A$ with non-standard growth controlled by an $N$-function depending on time and spatial variable. We do not assume continuity in time for the $N$-function. Using an additional regularization effect coming from the equation, we establish the existence of weak solutions ...
Miroslav Bulíček, Piotr Gwiazda, Jakub Skrzeczkowski   +2 more
openaire   +2 more sources

Existence of Solutions for Inclusion Problems in Musielak‐Orlicz‐Sobolev Space Setting

Journal of Function Spaces, Volume 2023, Issue 1, 2023., 2023
In this paper, we mainly prove the existence of (weak) solutions of an inclusion problem with the Dirichlet boundary condition of the following form: L ∈ A(x, u, Du) + F(x, u, Du), in Ω, and u = 0, on ∂Ω, in Musielak‐Orlicz‐Sobolev spaces W01LΦΩ by using the surjective theorem, where Ω ⊂ ℝN is a bounded Lipschitz domain, L belongs to the dual space ...
Ge Dong, Xiaochun Fang, Serena Matucci
wiley   +1 more source

Smoothness of the Orlicz norm in Musielak–Orlicz function spaces [PDF]

Mathematische Nachrichten, 2013
In this paper, we present a characterization of support functionals and smooth points in , the Musielak–Orlicz space equipped with the Orlicz norm. As a result, criterion for the smoothness of is also obtained. Some expressions involving the norms of functionals in , the topological dual of , are proved for arbitrary Musielak–Orlicz functions.
Vigelis, Rui F., Cavalcante, Charles C.
openaire   +2 more sources

Parametric superlinear double phase problems with singular term and critical growth on the boundary

Mathematical Methods in the Applied Sciences, Volume 45, Issue 4, Page 2276-2298, 15 March 2022., 2022
In this paper, we study quasilinear elliptic equations driven by the double phase operator along with a reaction that has a singular and a parametric superlinear term and with a nonlinear Neumann boundary condition of critical growth. Based on a new equivalent norm for Musielak–Orlicz Sobolev spaces and the Nehari manifold along with the fibering ...
Ángel Crespo‐Blanco, Nikolaos S. Papageorgiou, Patrick Winkert   +2 more
wiley   +1 more source

The Kellogg property under generalized growth conditions

Mathematische Nachrichten, Volume 295, Issue 2, Page 345-362, February 2022., 2022
Abstract We study minimizers of the Dirichlet φ‐energy integral with generalized Orlicz growth. We prove the Kellogg property, the set of irregular points has zero capacity, and give characterizations of semiregular boundary points. The results are new ever for the special cases double phase and Orlicz growth.
Petteri Harjulehto, Jonne Juusti
wiley   +1 more source

The Chebyshev Set Problem in Riesz Space

Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022
In this paper, we mainly study the best approximation theory in Riesz space, which is not constructed by the norm, but only rely on the order structure. Based on the order structure, we propose the concept of the order best approximation in Riesz space and discuss some problems related to the order best approximation, including some sufficient and ...
Shengwei Wu, Jiarui Zhao, Yanyan Xu, Guanggui Chen, Na Cheng, Sebastian Król   +5 more
wiley   +1 more source

Dual of Modulation Spaces with Variable Smoothness and Integrability

Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022
In this article, we first give a proof for the denseness of the Schwartz class in the modulation spaces with variable smoothness and integrability. Then, we study the dual spaces of such modulation spaces.
Hua Zhu, Ozgur Ege
wiley   +1 more source

Variable λ‐Central Morrey Space Estimates for the Fractional Hardy Operators and Commutators

Journal of Mathematics, Volume 2022, Issue 1, 2022., 2022
This paper aims to show that the fractional Hardy operator and its adjoint operator are bounded on central Morrey space with variable exponent. Similar results for their commutators are obtained when the symbol functions belong to λ‐central bounded mean oscillation (λ‐central BMO) space with variable exponent.
Amjad Hussain, Muhammad Asim, Fahd Jarad, Valerii Obukhovskii   +3 more
wiley   +1 more source

Solution and Stability of Quartic Functional Equations in Modular Spaces by Using Fatou Property

Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022
We propose a novel generalized quartic functional equation and investigate its Hyers–Ulam stability in modular spaces using a fixed point technique and the Fatou property in this paper.
N. Uthirasamy, K. Tamilvanan, Hemant Kumar Nashine, Reny George, Richard I. Avery   +4 more
wiley   +1 more source