Asymptotics for a Class of Non-Linear Evolution Equations, with Applications to Geometric Problems

1983/11/01 by Leon Simon · 792 citations
Mathematics · Computer Science · #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Advanced Mathematical Modeling in Engineering #Mathematics #Class (philosophy) #Applied mathematics #Pure mathematics #Computer science #Artificial intelligence

paper · doi:10.2307/2006981

published in Annals of Mathematics 118(3), 525 (Princeton University)

openalex publication_date 1983/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/18

Abstract

Soit Σ une variete de Riemann compacte et soit une fonction reguliere u=u(x,t), (x,t)∈ΣX(0,T) (T>0) satisfaisant une equation d'evolution soit de la forme ci-#7B-M(u)=f soit de la forme −u+u˙-#7B-M(u)-#7B-R(u)=f. (#7B-M(u) est l'operateur d'Euler-Lagrange d'ordre 2). On etudie le comportement asymptotique des solutions de ces equations

Citations

• A regularity theory for harmonic maps
• Multiple Integrals in the Calculus of Variations
• Elliptic Partial Differential Equations of Second Order
• Harmonic Mappings of Riemannian Manifolds
• On Homotopic Harmonic Maps
• Sobolev and mean‐value inequalities on generalized submanifolds of R n
• On the First Variation of a Varifold
• The singular sets of area minimizing rectifiable currents with codimension one and of area minimizing flat chains modulo two with arbitrary codimension

Cited by

• Nodal sets for solutions of elliptic equations
• Leon Simon [wikipedia]