REGULARITY RESULTS FOR VECTOR FIELDS OF BOUNDED
DISTORTION AND APPLICATIONS
A. FIORENZA AND
DIPARTIMENTO DI COSTRUZIONI E METODI MATEMATICI
MATEMATICA E APPLICAZIONI
VIA CINTIA, 80126~NAPOLI, ITALY
Received 17 January, 2000; accepted 4 April 2000.
Communicated by: S.
ABSTRACT. In this paper we prove higher integrability results for
vector fields ,
satisfying a "reverse" inequality of the type
Applications to the theory of quasiconformal mappings and
partial differential equations are given.
In particular, we prove regularity results for very weak solutions of
equations of the type
, in the homogeneous case, our method provides
a new proof of the regularity result
where is sufficiently small.
A result of higher integrability for functions verifying a reverse
integral inequality is used, and its optimality is proved.
Inequalities, Finite Distortion Vector
Vector Fields, Elliptic Partial Differential Equations
2000 Mathematics Subject