TY - JOUR
T1 - A geometric inequality for stable solutions of semilinear elliptic problems in the Engel group
AU - Pinamonti, Andrea
AU - Valdinoci, Enrico
PY - 2012/1/1
Y1 - 2012/1/1
N2 - We prove that, if E is the Engel group and u is a stable solution of ΔEu = f(u), then for any test function η ∈ C∞0 (E). Here above, h is the horizontal mean curvature, p is the imaginary curvature and J:= 2(X3X2uX1u - X3X1uX2u) + (X4u)(X1u - X2u) This can be interpreted as a geometric Poincaré inequality, extending the work of [21,22, 13] to stratified groups of step 3. As an application, we provide a non-existence result.
AB - We prove that, if E is the Engel group and u is a stable solution of ΔEu = f(u), then for any test function η ∈ C∞0 (E). Here above, h is the horizontal mean curvature, p is the imaginary curvature and J:= 2(X3X2uX1u - X3X1uX2u) + (X4u)(X1u - X2u) This can be interpreted as a geometric Poincaré inequality, extending the work of [21,22, 13] to stratified groups of step 3. As an application, we provide a non-existence result.
KW - Non-existence results
KW - Rigidity property
KW - Symmetry
UR - http://www.scopus.com/inward/record.url?scp=84873313641&partnerID=8YFLogxK
U2 - 10.5186/aasfm.2012.3733
DO - 10.5186/aasfm.2012.3733
M3 - Article
AN - SCOPUS:84873313641
SN - 1239-629X
VL - 37
SP - 357
EP - 373
JO - Annales Academiae Scientiarum Fennicae Mathematica
JF - Annales Academiae Scientiarum Fennicae Mathematica
IS - 1
ER -