Unique continuation for |Δu| ≤ V |∇u| and related problems.

Wolff, Thomas H.. "Unique continuation for |Δu| ≤ V |∇u| and related problems.." Revista Matemática Iberoamericana 6.3-4 (1990): 155-200. <http://eudml.org/doc/39399>.

@article{Wolff1990,
abstract = {Much of this paper will be concerned with the proof of the followingTheorem 1. Suppose d ≥ 3, r = max \{d, (3d - 4)/2\}. If V ∈ Llocr(Rd), then the differential inequality |Δu| ≤ V |∇u| has the strong unique continuation property in the following sense: If u belongs to the Sobolev space Wloc2,p and if |Δu| ≤ V |∇u| andlimR→0 R-N ∫|x| &lt; R |∇u|p' = 0for all N then u is constant.},
author = {Wolff, Thomas H.},
journal = {Revista Matemática Iberoamericana},
keywords = {Transformada de Laplace; Desigualdades; Formas diferenciales; Gradientes; Continuidad; Espacios de Sobolev; Unicidad; Carleman inequality; unique continuation},
language = {eng},
number = {3-4},
pages = {155-200},
title = {Unique continuation for |Δu| ≤ V |∇u| and related problems.},
url = {http://eudml.org/doc/39399},
volume = {6},
year = {1990},
}

TY - JOUR
AU - Wolff, Thomas H.
TI - Unique continuation for |Δu| ≤ V |∇u| and related problems.
JO - Revista Matemática Iberoamericana
PY - 1990
VL - 6
IS - 3-4
SP - 155
EP - 200
AB - Much of this paper will be concerned with the proof of the followingTheorem 1. Suppose d ≥ 3, r = max {d, (3d - 4)/2}. If V ∈ Llocr(Rd), then the differential inequality |Δu| ≤ V |∇u| has the strong unique continuation property in the following sense: If u belongs to the Sobolev space Wloc2,p and if |Δu| ≤ V |∇u| andlimR→0 R-N ∫|x| &lt; R |∇u|p' = 0for all N then u is constant.
LA - eng
KW - Transformada de Laplace; Desigualdades; Formas diferenciales; Gradientes; Continuidad; Espacios de Sobolev; Unicidad; Carleman inequality; unique continuation
UR - http://eudml.org/doc/39399
ER -