Flattening Results for Elliptic PDEs in Unbounded Domains with Applications to Overdetermined Problems

作者:Farina Alberto*; Valdinoci Enrico
来源:Archive for Rational Mechanics and Analysis, 2010, 195(3): 1025-1058.
DOI:10.1007/s00205-009-0227-8

摘要

Semilinear elliptic PDEs are dealt with, either in the half-space or in overdetermined settings. We obtain several new results and also give new proofs of celebrated theorems by exploiting some geometric analysis of level sets, a geometric inequality and a pointwise gradient estimate.

  • 出版日期2010-3