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A gradient bound and a liouville theorem for nonlinear poisson equations
Author(s) -
Modica Luciano
Publication year - 1985
Publication title -
communications on pure and applied mathematics
Language(s) - French
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160380515
Subject(s) - mathematics , poisson distribution , upper and lower bounds , citation , nonlinear system , calculus (dental) , mathematical economics , algebra over a field , discrete mathematics , pure mathematics , mathematical analysis , computer science , library science , statistics , physics , quantum mechanics , medicine , dentistry
Soit F∈C 2 (R) une fonction non negative et u∈C 3 (R n ) une solution dans tout R n de l'equation Δu=f(u), ou f=F' est la derivee 1ere de F. Si u est borne sur R n et s'il existe x 0 ∈R n tel que F(u(x 0 ))=0, alors u est constante