Now showing items 1-6 of 6

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

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(2014-12-31)
Let H ‚àà C 2(‚ÑùN√ón), H ‚â• 0. The PDE system (Formula presented.) arises as the Euler-Lagrange PDE of vectorial variational problems for the functional E ‚àû(u, Œ©) = {norm of matrix}H(Du){norm of matrix}L ‚àû(Œ©) defined ...
• #### The subelliptic ∞-Laplace system on Carnot-Carathéodory spaces ﻿

(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 +