TY - JOUR
T1 - 1D symmetry for solutions of semilinear and quasilinear elliptic equations
AU - Farina, Alberto
AU - Valdinoci, Enrico
PY - 2011/2/1
Y1 - 2011/2/1
N2 - Several new 1D results for solutions of possibly singular or degenerate elliptic equations, inspired by a conjecture of De Giorgi, are provided. In particular, 1D symmetry is proven under the assumption that either the profiles at infinity are 2D, or that one level set is a complete graph, or that the solution is minimal or, more generally, Q-minimal.
AB - Several new 1D results for solutions of possibly singular or degenerate elliptic equations, inspired by a conjecture of De Giorgi, are provided. In particular, 1D symmetry is proven under the assumption that either the profiles at infinity are 2D, or that one level set is a complete graph, or that the solution is minimal or, more generally, Q-minimal.
UR - http://www.scopus.com/inward/record.url?scp=78651299041&partnerID=8YFLogxK
U2 - 10.1090/S0002-9947-2010-05021-4
DO - 10.1090/S0002-9947-2010-05021-4
M3 - Article
AN - SCOPUS:78651299041
SN - 0002-9947
VL - 363
SP - 579
EP - 609
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 2
ER -