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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].

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