caa a22 4500 465819915 CHVBK 20180323112133.0 cr unu---uuuuu 170327e19901201xx s 000 0 eng 10.1007/BF01766983 doi (NATIONALLICENCE)springer-10.1007/BF01766983 L p -estimates for the solutions of second order elliptic equations [Elektronische Daten] [Franco Mandras, Giovanni Porru] Summary: We investigate the homogeneous Dirichlet problem in H2,p for a second order elliptic partial differential equation in nondivergence form Lu=f in the case in which the leading coefficients of L belong to H1,n(Ω), Ω ⊂ Rn. We prove that if p belongs to a suitable neighbourhood of 2, then the above problem, has a unique solution u satisfying ∥D2u∥p⩽ C∥f∥p; furthermore, if f ε Hk,p, k=1,2, ..., and the coefficients of L satisfy some natural conditions, then the solution satisfies $$\left\| u \right\|_{H^{k + 2,p} } \leqslant C\left\| f \right\|_{H^{k,p} }$$ . Fondazione Annali di Matematica Pura ed Applicata, 1990 Mandras Franco Dipartimento di Matematica, Via Ospedale 72, 09124, Cagliari, Italy aut Porru Giovanni Dipartimento di Matematica, Via Ospedale 72, 09124, Cagliari, Italy aut Annali di Matematica Pura ed Applicata Springer-Verlag 156/1(1990-12-01), 253-263 0373-3114 156:1<253 1990 156 10231 https://doi.org/10.1007/BF01766983 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01766983 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Mandras Franco Dipartimento di Matematica, Via Ospedale 72, 09124, Cagliari, Italy aut NATIONALLICENCE 700 1- Porru Giovanni Dipartimento di Matematica, Via Ospedale 72, 09124, Cagliari, Italy aut NATIONALLICENCE 773 0- Annali di Matematica Pura ed Applicata Springer-Verlag 156/1(1990-12-01), 253-263 0373-3114 156:1<253 1990 156 10231 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer