Related papers: Espaces d'Orlicz, Orlicz-Sobolev et application au…
We study unbounded weak supersolutions of elliptic partial differential equations with generalized Orlicz (Musielak--Orlicz) growth. We show that they satisfy the weak Harnack inequality with optimal exponent provided that they belong to a…
In this paper, we study a new class of fractional partial differential equations which are obtained by minimizing variational problems in fractional Sobolev spaces. We introduce a notion of fractional gradient which has the potential to…
Sobolev spaces are a natural framework for the analysis of problems in partial differential equations and calculus of variations. Some physical and geometric contexts, such as liquid crystals models and harmonic maps, lead to consider…
In this paper we extend the theory of Henstock-Orlicz spaces with respect to vector measure. We study the integral representation of operators. Lastly we study Uniformly convexity, reflexivity and the Radon-Nikodym property of the…
In this paper we study the necessary and sufficient conditions on domain for Musielak-Orlicz-Sobolev embedding of the space $W^{1,\Phi(\cdot,\cdot)}(\Omega)$ where $\Phi(x,t):=t^{p(x)}{(\log(e+t))}^{q(x)}.$
The field of partial differential equations (PDEs) is vast in size and diversity. The basic reason for this is that essentially all fundamental laws of physics are formulated in terms of PDEs. In addition, approximations to these…
In the present paper we provide some equivalent conditions for composition operators to have shadowing property on Orlicz space. Also, we obtain that for the composition operators on Orlicz spaces the notions of generalized hyperbolicity…
In this article, the authors introduce the spaces of Lipschitz type on spaces of homogeneous type in the sense of Coifman and Weiss, and discuss their relations with Besov and Triebel-Lizorkin spaces. As an application, the authors…
We consider Littlewood-Paley functions associated with non-isotropic dilations. We prove that they can be used to characterize the parabolic Hardy spaces of Calder\'{o}n-Torchinsky.
We prove capacitary strong type inequalities for functions belonging to Orlicz-Sobolev spaces. As an application we consider capacitary averages and their limits.
A generalization of the Pistone-Sempi argument, demonstrating the utility of non-commutative Orlicz spaces, is presented. The question of lifting positive maps defined on von Neumann algebra to maps on corresponding noncommutative Orlicz…
An H^p-theory of quasiconformal mappings on B^n has already been established. By replacing t^p with a general increasing growth function {\psi}(t) we define the Hardy-Orlicz spaces of quasiconformal mappings and prove various…
We present a new solver for coupled nonlinear elliptic partial differential equations (PDEs). The solver is based on pseudo-spectral collocation with domain decomposition and can handle one- to three-dimensional problems. It has three…
We investigate robust Orlicz spaces as a generalisation of robust $L^p$-spaces. Two constructions of such spaces are distinguished, a top-down approach and a bottom-up approach. We show that separability of robust Orlicz spaces or their…
In this article we investigate the Fourier series and transforms for the functions defined on the $ [0, 2 \pi]^ d $ or $ R^d $ and belonging to the exponential Orlicz and some other rearrangement invariant (r.i.) spaces.
In this paper we study Strichartz estimates for dispersive equations which are defined by radially symmetric pseudo-differential operators, and of which initial data belongs to spaces of Sobolev type defined in spherical coordinates. We…
There are many numerical methods for solving partial different equations (PDEs) on manifolds such as classical implicit, finite difference, finite element, and isogeometric analysis methods which aim at improving the interoperability…
This paper deals with the solution of large classes of systems of nonlinear partial differential equations (PDEs) in spaces of generalized functions that are constructed as the completion of uniform convergence spaces. The existence result…
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.…
In this paper, we study the sharp Poincar\'e inequality and the Sobolev inequalities in the higher order Lorentz--Sobolev spaces in the hyperbolic spaces. These results generalize the ones obtained in \cite{Nguyen2020a} to the higher order…