On infinitesimal and local rigidity of harmonic maps between spheres defined by spherical harmonics

On the Regularity of Harmonic Functions

On the Regularity of Harmonic Functions and Spherical Harmonic Maps Defined on Lattices

✍ Lawrence E. Thomas 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 140 KB

A growth lemma for certain discrete symmetric Laplacians defined on a lattice Z d δ = δZ d ⊂ R d with spacing δ is proved. The lemma implies a De Giorgi theorem, that the harmonic functions for these Laplacians are equi-Hölder continuous, δ → 0. These results are then applied to establish regularity