Everywhere regularity theorems for mappings which minimize $p$-energy
Martín Fuchs · Czech digital mathematics library · 1987
AbstracttWe consider functions uiO -* TT defined on some n-dlmenslonal region taking values in the closure of a smooth domain M located in Euclidean space or a Riemannian manifold which locally minimize a degenerate functional of the formX|0u| p (p*2) under this nonlinear side condition.While the partial regularity theory was developed in If 1,23, we study here geometric conditions on M which exclude singular points.Key words* p-harmonic problems for vector functions, degenerate functionals, regularity of minimiters, removable singularities, blow-up technique* •obstacle problems. ClassiflcaUom Primary 49Secondary 35010 0. IntroducUon end results.In this section we fix our asa|imptions and state the main resultst Let 0 denote a bounded open subset of an n-dimensional manifold X, n*2; moreover we are given an N-dimensional Riemannian mani fold Y embedded in a Euclidean space lr\ Suppose further that M is a domain with smooth boundary and compact closure in Y.For a real number p£2 and functions u in the Sobolev space H * p (D,lc) we intrortj.eethe p-energy