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.

A geometric inequality for stable solutions of semilinear elliptic problems in the Engel group / A. Pinamonti, E. Valdinoci. - In: ANNALES ACADEMIAE SCIENTIARUM FENNICAE. MATHEMATICA. - ISSN 1239-629X. - 37:2(2012), pp. 357-373. [10.5186/aasfm.2012.3733]

A geometric inequality for stable solutions of semilinear elliptic problems in the Engel group

E. Valdinoci
Ultimo
2012

Abstract

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.
Rigidity property ; symmetry ; non-existence results
Settore MAT/05 - Analisi Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/224006
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