Wyniki wyszukiwania dla: ANISOTROPIC ORLICZ SPACE

• On the Fenchel–Moreau conjugate of G-function and the second derivative of the modular in anisotropic Orlicz spaces

  Publikacja

  • J. Maksymiuk

  - CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS - Rok 2024

  In this paper, we investigate the properties of the Fenchel–Moreau conjugate of G-function with respect to the coupling function c(x, A) = |A[x]2 |. We provide conditions that guarantee that the conjugate is also a G-function. We also show that if a G-function G is twice differentiable and its second derivative belongs to the Orlicz space generated by the Fenchel–Moreau conjugate of G then the modular generated by G is twice differentiable...

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• Mountain pass type periodic solutions for Euler–Lagrange equations in anisotropic Orlicz–Sobolev space

  Publikacja

  • M. Chmara
  • J. Maksymiuk

  - JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS - Rok 2019

  Using the Mountain Pass Theorem, we establish the existence of periodic solution for Euler–Lagrange equation. Lagrangian consists of kinetic part (an anisotropic G-function), potential part and a forcing term. We consider two situations: G satisfying at infinity and globally. We give conditions on the growth of the potential near zero for both situations.

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• Anisotropic Orlicz–Sobolev spaces of vector valued functions and Lagrange equations

  Publikacja

  • M. Chmara
  • J. Maksymiuk

  - JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS - Rok 2017

  In this paper we study some properties of anisotropic Orlicz and Orlicz–Sobolev spaces of vector valued functions for a special class of G-functions. We introduce a variational setting for a class of Lagrangian Systems. We give conditions which ensure that the principal part of variational functional is finitely defined and continuously differentiable on Orlicz–Sobolev space.

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• Mountain pass solutions to Euler-Lagrange equations with general anisotropic operator

  Publikacja

  • M. Chmara
  • J. Maksymiuk

  - JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS - Rok 2020

  Using the Mountain Pass Theorem we show that the problem \begin{equation*} \begin{cases} \frac{d}{dt}\Lcal_v(t,u(t),\dot u(t))=\Lcal_x(t,u(t),\dot u(t))\quad \text{ for a.e. }t\in[a,b]\\ u(a)=u(b)=0 \end{cases} \end{equation*} has a solution in anisotropic Orlicz-Sobolev space. We consider Lagrangian $\Lcal=F(t,x,v)+V(t,x)+\langle f(t), x\rangle$ with growth conditions determined by anisotropic G-function and some geometric conditions...

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• Existence of Two Periodic Solutions to General Anisotropic Euler-Lagrange Equations

  Publikacja

  • M. Chmara

  - TAIWANESE JOURNAL OF MATHEMATICS - Rok 2021

  Abstract. This paper is concerned with the following Euler-Lagrange system d/dtLv(t,u(t), ̇u(t)) =Lx(t,u(t), ̇u(t)) for a.e.t∈[−T,T], u(−T) =u(T), Lv(−T,u(−T), ̇u(−T)) =Lv(T,u(T), ̇u(T)), where Lagrangian is given by L=F(t,x,v) +V(t,x) +〈f(t),x〉, growth conditions aredetermined by an anisotropic G-function and some geometric conditions at infinity.We consider two cases: with and without forcing termf. Using a general version...

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• Adam Dąbrowski dr inż.

  Osoby

  Adam Dąbrowski uzyskał stopień doktora nauk inżynieryjno-technicznych w dyscyplinie inżynieria mechaniczna na Politechnice Gdańskiej oraz ukończył studia II stopnia na kierunku mechatronika na Technische Universität Hamburg a także double degree Engineering and Management of Space Systems na Hochschule Bremen. Posiada doświadczenie przemysłowe (Instytut Lotnictwa w Warszawie, SICK AG w Hamburgu, Blue Dot Solutions w Gdańsku, Niemieckie...

• Sociology of Space

  Kursy Online

  • M. Dymnicka

  The course is aimed at discussing the significance of the city as a topic of sociological analysis. During the seminar students will discuss the relation between sociology, architecture and space. Moreover, the debate will touch on the field of culture and its role in (re)creating and (re)constructing space. Discussions will also be related to the aspect of interactions in time and space. Contemporary dilemmas and challenges in...

• Regularity of weak solutions for aclass of elliptic PDEs in Orlicz-Sobolev spaces

  Publikacja

  • J. Maksymiuk
  • K. Wroński

  - Topological Methods in Nonlinear Analysis - Rok 2020

  We consider the elliptic partial differential equation in the divergence form $$-\div(\nabla G(\nabla u(x))) t + F_u (x, u(x)) = 0,$$ where $G$ is a convex, anisotropic function satisfying certain growth and ellipticity conditions We prove that weak solutions in $W^{1,G}$ are in fact of class $W^{2,2}_{loc}\cap W^{1,\infty}_{loc}$.

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• Laplace domain BEM for anisotropic transient elastodynamics

  Publikacja

  • I. Markov
  • L. A. Igumnov
  • A. Belov
  • V. Eremeev

  - MATHEMATICS AND MECHANICS OF SOLIDS - Rok 2022

  In this paper, we describe Laplace domain boundary element method (BEM) for transient dynamic problems of three-dimensional finite homogeneous anisotropic linearly elastic solids. The employed boundary integral equations for displacements are regularized using the static traction fundamental solution. Modified integral expressions for the dynamic parts of anisotropic fundamental solutions and their first derivatives are obtained....

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• Przestrzeń Społeczna (Social Space)

  Czasopisma

  ISSN: 2084-7696 , eISSN: 2084-1558