Summary: Calc. Var. 2, 1-16 (1994)
@ Springer-Verlag 1994
A transmission problem in the calculus of variations
E. Acerbi 1 and N. Fusco 2
1 Dipartimento di Matematica, V. D'Azeglio 85, 1-43100 Parma, Italy
2 Dipartimento di Matematica e Appl., Complesso M. S. Angelo, V. Cinthia, 1-80121 Napoli, Italy
Received March 24, 1993/Accepted April 27, 1993
Abstract. We study h61der regularity of minimizers of the functional fs? [Dul p(x)dx,
where p(x) takes only two values and jumps across a Lipschitz surface. No restriction
on the two values is imposed.
Mathematics Subject Classification." 49N60, 35B85, 73V25
Many classical results concern the regularity of minimizers u of
r F(x, Du) dx,
where F satisfies the standard growth conditions
(1) ]z]p<_F(x,z)<_c(l+Izl p) for somep> 1.
Following an example by Giaquinta , see also ,, several papers appeared in
which (1) is replaced by
Izlp <_F(x,z) <_c(l + lzlq) for someq>p> 1.
Most of these deal with anisotropic (but essentially homogeneous) situations, as e.g.