Now showing items 1-6 of 6

    • Explicit 2D ∞-harmonic maps whose interfaces have junctions and corners 

      Katzourakis, N.I. (2013-12-31)
      Given a map u:Ω⊆Rn→RN, the ∞-Laplacian is the system:(1)δ∞u:=(Du⊗Du+|Du|2[Du]⊥⊗I):D2u=0 and arises as the "Euler-Lagrange PDE" of the supremal functional E∞(u,Ω)={norm of matrix}Du{norm of matrix}L∞(Ω). (1) is the model ...
    • Explicit singular viscosity solutions of the Aronsson equation 

      Katzourakis, N.I. (2011-12-31)
      We establish that when n≥2 and H∈C1(Rn) is a Hamiltonian such that some level set contains a line segment, the Aronsson equation D2u:Hp(Du)⊗Hp(Du)=0 admits explicit entire viscosity solutions. They are superpositions of a ...
    • L ∞ variational problems for maps and the Aronsson PDE system 

      Katzourakis, N.I. (2012-12-31)
      By employing Aronsson's absolute minimizers of L ∞ functionals, we prove that absolutely minimizing maps u:Rn→RN solve a "tangential" Aronsson PDE system. By following Sheffield and Smart (2012) [24], we derive δ ∞ with ...
    • Maximum Principles for vectorial approximate minimizers of nonconvex functionals 

      Katzourakis, N.I. (2013-12-31)
      We establish Maximum Principles which apply to vectorial approximate minimizers of the general integral functional of Calculus of Variations. Our main result is a version of the Convex Hull Property. The primary advance ...
    • On the Structure of $\infty$-Harmonic Maps 

      Katzourakis, N.I. (2014-12-31)
      Let H ∈ C 2(ℝN×n), H ≥ 0. The PDE system (Formula presented.) arises as the Euler-Lagrange PDE of vectorial variational problems for the functional E ∞(u, Ω) = {norm of matrix}H(Du){norm of matrix}L ∞(Ω) defined ...
    • The subelliptic ∞-Laplace system on Carnot-Carathéodory spaces 

      Katzourakis, N.I. (2013-12-31)
      Given a Carnot-Carathéodory space Ω ⊆ ℝn with associated frame of vector fields X = {X<inf>1</inf>,⋯, X<inf>m</inf>}, we derive the subelliptic ∞-Laplace system for mappings u: Ω → ℝN, which reads δX∞u:=(Xu ⊗ Xu +