caa a22 4500 465820034 CHVBK 20180323112133.0 cr unu---uuuuu 170327e19901201xx s 000 0 eng 10.1007/BF01766975 doi (NATIONALLICENCE)springer-10.1007/BF01766975 Naumann Joachim Sektion Mathematik, Humboldt-Universität zu Berlin, PSF 1297, 1086, Berlin, DDR aut Interior integral estimates on weak solutions of certain degenerate elliptic systems [Elektronische Daten] [Joachim Naumann] Summary: We prove the existence of second order derivatives of any weak solution of the system $$\frac{\partial }{{\partial x_\alpha }}A_i^\alpha (\nabla u) = 0(i = 1,...,N)$$ under very mild conditions on the functions A i α . These conditions include the special case: A i α (ξ)=0 if ξ=0, A i α (ξ)=|ξ|p−2ξ i α if ξ≠0 (ξ∈ℝnN;α=1,...,n,i=1,...,N;1<p<2). Under a stronger condition on A i α we establish an appropriate Caccioppoli inequality which enables us to prove the integrability of (1+|∇u|2)(p−1)/4 ∇2u to a certain power t > 2. Fondazione Annali di Matematica Pura ed Applicata, 1990 Annali di Matematica Pura ed Applicata Springer-Verlag 156/1(1990-12-01), 113-125 0373-3114 156:1<113 1990 156 10231 https://doi.org/10.1007/BF01766975 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01766975 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Naumann Joachim Sektion Mathematik, Humboldt-Universität zu Berlin, PSF 1297, 1086, Berlin, DDR aut NATIONALLICENCE 773 0- Annali di Matematica Pura ed Applicata Springer-Verlag 156/1(1990-12-01), 113-125 0373-3114 156:1<113 1990 156 10231 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer