@unpublished{MeraTarkhanov2016, author = {Mera, Azal and Tarkhanov, Nikolai Nikolaevich}, title = {The Neumann problem after Spencer}, volume = {5}, number = {6}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-90631}, pages = {21}, year = {2016}, abstract = {When trying to extend the Hodge theory for elliptic complexes on compact closed manifolds to the case of compact manifolds with boundary one is led to a boundary value problem for the Laplacian of the complex which is usually referred to as Neumann problem. We study the Neumann problem for a larger class of sequences of differential operators on a compact manifold with boundary. These are sequences of small curvature, i.e., bearing the property that the composition of any two neighbouring operators has order less than two.}, language = {en} } @unpublished{MeraShlapunovTarkhanov2015, author = {Mera, Azal and Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich}, title = {Navier-Stokes equations for elliptic complexes}, volume = {4}, number = {12}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-85592}, pages = {27}, year = {2015}, abstract = {We continue our study of invariant forms of the classical equations of mathematical physics, such as the Maxwell equations or the Lam{\´e} system, on manifold with boundary. To this end we interpret them in terms of the de Rham complex at a certain step. On using the structure of the complex we get an insight to predict a degeneracy deeply encoded in the equations. In the present paper we develop an invariant approach to the classical Navier-Stokes equations.}, language = {en} }