Druet (Ann. Inst. H. Poincaré Anal. Non Linèaire 19(2) (2002) 125) solved two conjectures proposed by Haim Brezis (Comm. Pure Appl. Math. 39 (1986) 17) about “low”-dimension phenomena for some elliptic problem with critical Sobolev exponent. In Druet (Ann. Inst. H. Poincaré Anal. Non Linèaire 19(2) (2002) 125), the proof of one of the two conjectures is reduced to an asymptotic analysis which is carried over with very general techniques involving pointwise estimates. We propose here a different and simpler approach in the blow-up analysis based on integral estimates and on a careful expansion of the energy functional.
Esposito, P. (2004). On some conjectures proposed by Haïm Brezis. NONLINEAR ANALYSIS, 56(5), 751-759 [10.1016/j.na.2003.10.012].
On some conjectures proposed by Haïm Brezis
ESPOSITO, PIERPAOLO
2004-01-01
Abstract
Druet (Ann. Inst. H. Poincaré Anal. Non Linèaire 19(2) (2002) 125) solved two conjectures proposed by Haim Brezis (Comm. Pure Appl. Math. 39 (1986) 17) about “low”-dimension phenomena for some elliptic problem with critical Sobolev exponent. In Druet (Ann. Inst. H. Poincaré Anal. Non Linèaire 19(2) (2002) 125), the proof of one of the two conjectures is reduced to an asymptotic analysis which is carried over with very general techniques involving pointwise estimates. We propose here a different and simpler approach in the blow-up analysis based on integral estimates and on a careful expansion of the energy functional.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
