caa a22 4500 475740939 CHVBK 20180406123459.0 cr unu---uuuuu 170329e20001101xx s 000 0 eng 10.1023/A:1026660700355 doi (NATIONALLICENCE)springer-10.1023/A:1026660700355 Weak Solvability of the Dirichlet Problem on Stratified Sets [Elektronische Daten] [O. Penkin, E. Bogatov] The Dirichlet problem is posed for an analog of the Beltrami--Laplace operator on sets consisting of manifolds of various dimensions regularly adjacent to one another (stratified sets). A special system of notions permits one to prove analogs of Green's integral identities and the Poincaré inequality for Sobolev type spaces. The weak solvability of the Dirichlet problem for this operator, as well as for an analog of the biharmonic operator, is proved on the basis of the Riesz theorem on the representation of linear functionals. Plenum Publishing Corporation, 2000 stratified set nationallicence Dirichlet problem nationallicence Laplace operator nationallicence biharmonic operator nationallicence Sobolev space nationallicence weak solvability nationallicence Green formula nationallicence Poincaré inequality nationallicence Penkin O. Voronezh State University, Russia aut Bogatov E. Voronezh State University, Russia aut Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 68/5-6(2000-11-01), 740-750 0001-4346 68:5-6<740 2000 68 11006 https://doi.org/10.1023/A:1026660700355 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1026660700355 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Penkin O. Voronezh State University, Russia aut NATIONALLICENCE 700 1- Bogatov E. Voronezh State University, Russia aut NATIONALLICENCE 773 0- Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 68/5-6(2000-11-01), 740-750 0001-4346 68:5-6<740 2000 68 11006 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer