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MARCO SQUASSINA

Professore ordinario

Facoltà di SCIENZE MATEMATICHE, FISICHE E NATURALI

Sede di  Brescia

Dipartimento di Matematica e fisica - Niccolò Tartaglia

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Tel. +39 (0)30 2406.712
Fax. +39 (0)30 2406.742
e-mail: marco.squassina@unicatt.it
Contatto skype: marco.squassina
Sito web personale: www.dmf.unicatt.it/~squassin

Principali Pubblicazioni

Articoli su riviste scientifiche

Existence and nonexistence results for critical growth biharmonic elliptic problems

AUTORE

Gazzola, F.; Grunau, H. C.; Squassina, Marco

ANNO DI PUBBLICAZIONE

2003

TITOLO PERIODICO

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS

PAGINE PERIODICO

117 - 143

We prove existence of nontrivial solutions to semilinear fourth order problems
at critical growth in some contractible domains which are perturbations of small capacity of
domains having nontrivial topology. Compared with the second order case, some difficulties
arise which are overcome by a decomposition method with respect to pairs of dual cones.
In the case of Navier boundary conditions, further technical problems have to be solved by
means of a careful application of concentration compactness lemmas. The required generalization
of a Struwe type compactness lemma needs a somehow involved discussion of certain
limit procedures. Also nonexistence results for positive solutions in the ball are obtained,
extending a result of Pucci and Serrin on so-called critical dimensions to Navier boundary
conditions. A Sobolev inequality with optimal constant and remainder term is proved, which
is closely related to the critical dimension phenomenon. Here, this inequality serves as a tool
in the proof of the existence results and in particular in the discussion of certain relevant
energy levels.

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