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Dipartimento di Matematica -Politecnico di Torino April 1991 Partial Regularity

Summary: Dipartimento di Matematica - Politecnico di Torino April 1991
Partial Regularity
under Anisotropic (p,q) Growth Conditions
E. Acerbi and N. Fusco
1 . Introduction
In this paper we give a contribution to the study of the regularity of minimizers of
integral functionals of the kind
f(Du) dx under the assumption
(1.1) ||p
f() c(1 + ||q
Until recently it was customary to take
q = p,
but the question of whether regularity in the general case (1.1) could be obtained
remained open. In 1987 some examples were produced (see [7],[11]) that showed that
the answer to this question is in general negative. The example, as modified by [9],
shows that in the particular case of

+ |D1u|p1


Source: Acerbi, Emilio - Dipartimento di Matematica, UniversitÓ degli Studi di Parma
Fusco, Nicola - Dipartimento di Matematica e Applicazioni, UniversitÓ degli Studi di Napoli "Federico II"


Collections: Mathematics