TITLE

Generalised twists, stationary loops, and the Dirichlet energy over a space of measure preserving maps

AUTHOR(S)
Shahrokhi-Dehkordi, M.; Taheri, A.
PUB. DATE
June 2009
SOURCE
Calculus of Variations & Partial Differential Equations;Jun2009, Vol. 35 Issue 2, p191
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
Let $${\Omega \subset \mathbb{R}^n}$$ be a bounded Lipschitz domain and consider the Dirichlet energy functionalover the space of measure preserving mapsIn this paper we introduce a class of maps referred to as generalised twists and examine them in connection with the Euler�Lagrange equations associated with $${{\mathbb F}}$$ over $${{\mathcal A}(\Omega)}$$ . The main result here is that in even dimensions the latter equations admit infinitely many solutions, modulo isometries, amongst such maps. We investigate various qualitative properties of these solutions in view of a remarkably interesting previously unknown explicit formula.
ACCESSION #
36479338

 

Related Articles

  • Concentration phenomena in weakly coupled elliptic systems with critical growth*. Molle, Riccardo; Pistoia, Angela // Bulletin of the Brazilian Mathematical Society;Nov2004, Vol. 35 Issue 3, p395 

    In this paper we consider the weakly coupled elliptic system with critical growthwherea,b,c,dareC1-functions defined in a bounded regular domain O of RN. Here we construct families of solutions which blow-up and concentrate at some points in O as the positive parameter e goes to zero.

  • DIRICHLET PROBLEMS WITH SINGULAR AND GRADIENT QUADRATIC LOWER ORDER TERM. Boccardo, Lucio // ESAIM: Control, Optimisation & Calculus of Variations;Jul2008, Vol. 14 Issue 3, p411 

    We present a revisited form of a result proved in [Boccardo, Murat and Puel, Portugaliae Math. 41 (1982) 507-534] and then we adapt the new proof in order to show the existence for solutions of quasilinear elliptic problems also if the lower order term has quadratic dependence on the gradient...

  • A new fictitious domain method in shape optimization. Eppler, Karsten; Harbrecht, Helmut; Mommer, Mario S. // Computational Optimization & Applications;Jun2008, Vol. 40 Issue 2, p281 

    The present paper is concerned with investigating the capability of the smoothness preserving fictitious domain method from Mommer (IMA J. Numer. Anal. 26:503-524, 2006) to shape optimization problems. We consider the problem of maximizing the Dirichlet energy functional in the class of all...

  • Boundary Controllability of a Dynamical System Governed by the Wave Equation on a Class of Graphs (Trees). Belishev, M. // Journal of Mathematical Sciences;Jan2006, Vol. 132 Issue 1, p11 

    The boundary control problem for the wave equation on a planar graph consisting of strings of variable densities with Dirichlet control at boundary vertices is considered. The exact controllability in L2-classes of controls and states is established in the case where the graph is a tree; a sharp...

  • BLOW-UP FOR SEMILINEAR PARABOLIC EQUATIONS WITH CRITICAL SOBOLEV EXPONENT. LI MA // Communications on Pure & Applied Analysis;Mar2013, Vol. 12 Issue 2, p1103 

    In this paper, we study the global existence and blow-up results of semilinear parabolic equations with critical Sobolev exponent ut - Δu = |u|p-1 u, in Ω x (0, T) with the Dirichlet boundary condition u = 0 on the boundary ∂Ωx [0, T) and u = Φ at t = 0, where Ω ⊂ Rn...

  • Homogenization of monotone operators under conditions of coercitivity and growth of variable order. Zhikov, V.; Pastukhova, S. // Mathematical Notes;Aug2011, Vol. 90 Issue 1/2, p48 

    We obtain a homogenization procedure for the Dirichlet boundary-value problem for an elliptic equation of monotone type in the domain Ω ⊂ ℝ. The operator of the problem satisfies the conditions of coercitivity and of growth with variable order p( x) = p( x/ɛ); furthermore, p(...

  • PARTIAL DATA FOR THE NEUMANN-DIRICHLET MAGNETIC SCHRÖDINGER INVERSE PROBLEM. CHUNG, FRANCIS J. // Inverse Problems & Imaging;Nov2014, Vol. 8 Issue 4, p959 

    We show that an electric potential and magnetic field can be uniquely determined by partial boundary measurements of the Neumann-to-Dirichlet map of the associated magnetic Schrödinger operator. This improves upon the results in [4] by including the determination of a magnetic field. The main...

  • Quantization of theories with non-Lagrangian equations of motion. Gitman, D.; Kupriyanov, V. // Journal of Mathematical Sciences;Mar2007, Vol. 141 Issue 4, p1399 

    We present an approach to the canonical quantization of systems with non-Lagrangian equations of motion. We first construct an action principle for equivalent first-order equations of motion. Hamiltonization and canonical quantization of the constructed Lagrangian theory is a nontrivial problem,...

  • Why Lagrangians? Svetlichny, George // AIP Conference Proceedings;11/14/2007, Vol. 956 Issue 1, p120 

    We argue that Feynman's Integral imposes the condition of being mutually unbiased on pairs of bases that are causally proximal. This sheds light on the nature of Lagrangian theories from the emergent space-time perspective.

Share

Read the Article

Courtesy of VIRGINIA BEACH PUBLIC LIBRARY AND SYSTEM

Sign out of this library

Other Topics