On Transforms of Divergence-Free and Curl-Free Fields, Associated with Inverse Problems
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| 024 | 7 | 0 | |a 10.1007/s10958-015-2309-5 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10958-015-2309-5 | ||
| 100 | 1 | |a Demchenko |D M. |u St. Petersburg Department of the V. A. Steklov Institute of Mathematics of the Russian Academy of Sciences, St. Petersburg, Russia |4 aut | |
| 245 | 1 | 0 | |a On Transforms of Divergence-Free and Curl-Free Fields, Associated with Inverse Problems |h [Elektronische Daten] |c [M. Demchenko] |
| 520 | 3 | |a The M- and N-transforms acting, respectively, on divergence-free and curl-free vector fields on a Riemannian manifold with boundary are investigated. These transforms arise in studying the inverse problems of electrodynamics and elasticity theory. A divergence-free field is mapped by M to a field that is tangential to equidistants of the boundary. The N-transform maps a curl-free field to a field that is normal to equidistants. In preceding papers, the operators M and N were considered in the case of smooth equidistants, which is realized in a sufficiently small near-boundary layer. This allows one to consider transforms of fields supported in such a layer; it was proved that M and N are unitary in the corresponding spaces with L2-norms. In one of the papers, the case of fields on the whole manifold was considered, but almost all equidistants were assumed to be Lipschitz surfaces. It was proved that M is coisometric (i.e., the adjoint operator is isometric). In the present paper, the same result is obtained for both transforms in the general case with no constraints on equidistants at all. | |
| 540 | |a Springer Science+Business Media New York, 2015 | ||
| 773 | 0 | |t Journal of Mathematical Sciences |d Springer US; http://www.springer-ny.com |g 206/3(2015-04-01), 247-259 |x 1072-3374 |q 206:3<247 |1 2015 |2 206 |o 10958 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10958-015-2309-5 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10958-015-2309-5 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 100 |E 1- |a Demchenko |D M. |u St. Petersburg Department of the V. A. Steklov Institute of Mathematics of the Russian Academy of Sciences, St. Petersburg, Russia |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Journal of Mathematical Sciences |d Springer US; http://www.springer-ny.com |g 206/3(2015-04-01), 247-259 |x 1072-3374 |q 206:3<247 |1 2015 |2 206 |o 10958 | ||