zbMATH — the first resource for mathematics

Strong convergence of \(p\)-harmonic mappings. (English) Zbl 0833.35038
Chipot, M. (ed.) et al., Progress in partial differential equations: the Metz surveys 3. Proceedings of the conferences given at the University of Metz, France during the 1993 ”Metz Days”. Harlow: Longman Scientific & Technical. Pitman Res. Notes Math. Ser. 314, 58-64 (1994).
The authors study convergence properties of \(p\)-harmonic mappings, i.e. solutions of an equation of the form \[ \text{div}(|\nabla u|^{p- 2}\nabla u)+ f(u, \nabla u)= 0,\tag{\(*\)} \] where \(|f(u, \nabla u)|\leq C|\nabla u|^p\). They show that under certain conditions every sequence \(u_i\) of weak solutions of \((*)\) which is weakly convergent in \(W^{1, p}\), converges strongly in \(W^{1, q}\) for \(1< q< p\).
For the entire collection see [Zbl 0817.00012].

35J60 Nonlinear elliptic equations
35A35 Theoretical approximation in context of PDEs