Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 32, 2007, 27-53

BORDERLINE SHARP ESTIMATES FOR SOLUTIONS TO NEUMANN PROBLEMS

Angela Alberico and Andrea Cianchi

Istituto per le Applicazioni del Calcolo "M. Picone", Sez. Napoli - C.N.R.
Via P. Castellino 111, 80131 Napoli, Italy; a.alberico 'at' iac.cnr.it

Dipartimento di Matematica e Applicazioni per l'Architettura, Università di Firenze
Piazza Ghiberti 27, 50122 Firenze, Italy; cianchi 'at' unifi.it

Abstract. A priori estimates for solutions to homogeneous Neumann problems for uniformly elliptic equations in open subsets \Omega of Rⁿ are established, with data in the limiting space L^n/2(\Omega), or, more generally, in the Lorentz spaces L^n/2,q(\Omega). These estimates are optimal as far as either constants or norms are concerned.

2000 Mathematics Subject Classification: Primary 35B45, 35J25, 46E30.

Key words: Elliptic equations, boundary value problems, a priori estimates, Moser inequality, Orlicz spaces, Lorentz spaces.

Reference to this article: A. Alberico and A. Cianchi: Borderline sharp estimates for solutions to Neumann problems. Ann. Acad. Sci. Fenn. Math. 32 (2007), 27-53.

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