Browsing Past Topics (PT) by Author "Katzourakis, N.I."
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Explicit 2D ∞harmonic maps whose interfaces have junctions and corners
Katzourakis, N.I. (20131231)Given a map u:Ω⊆Rn→RN, the ∞Laplacian is the system:(1)δ∞u:=(Du⊗Du+Du2[Du]⊥⊗I):D2u=0 and arises as the "EulerLagrange 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. (20111231)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. (20121231)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. (20131231)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. (20141231)Let H ‚àà C 2(‚ÑùN√ón), H ‚â• 0. The PDE system (Formula presented.) arises as the EulerLagrange 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 CarnotCarathéodory spaces
Katzourakis, N.I. (20131231)Given a CarnotCarathéodory 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 +