TY - JOUR
T1 - Hodge decompositions with mixed boundary conditions and applications to partial differential equations on Lipschitz manifolds
AU - Gol'dshtein, V.
AU - Mitrea, I.
AU - Mitrea, M.
N1 - Funding Information:
The authors have been supported in part by the National Science Foundation Grants DMS-0653180, DMS/FRG-0456306, DMS 1048467. The second-named author has also been supported in part by the Ruth I. Michler Memorial Prize. Last but not least, we wish to thank Professor V. Maz’ya for several stimulating discussions and for his interest in our work.
PY - 2011/1/1
Y1 - 2011/1/1
N2 - We study boundary-value problems with mixed boundary conditions in weakly Lipschitz domains of compact boundaryless Riemannian Lipschitz manifolds. These include the case of the Maxwell system, the Hodge-Dirac operator, and the Hodge-Laplacian. Our approach brings to bear tools from functional analysis, differential geometry, harmonic analysis, and topology. Bibliography: 45 titles.
AB - We study boundary-value problems with mixed boundary conditions in weakly Lipschitz domains of compact boundaryless Riemannian Lipschitz manifolds. These include the case of the Maxwell system, the Hodge-Dirac operator, and the Hodge-Laplacian. Our approach brings to bear tools from functional analysis, differential geometry, harmonic analysis, and topology. Bibliography: 45 titles.
UR - http://www.scopus.com/inward/record.url?scp=78651295558&partnerID=8YFLogxK
U2 - 10.1007/s10958-010-0200-y
DO - 10.1007/s10958-010-0200-y
M3 - Article
AN - SCOPUS:78651295558
SN - 1072-3374
VL - 172
SP - 347
EP - 400
JO - Journal of Mathematical Sciences
JF - Journal of Mathematical Sciences
IS - 3
ER -