@unpublished{Tepoyan2008, author = {Tepoyan, Liparit}, title = {The mixed problem for a degenerate operator equation}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30334}, year = {2008}, abstract = {We consider a mixed problem for a degenerate differentialoperator equation of higher order. We establish some embedding theorems in weighted Sobolev spaces and show existence and uniqueness of the generalized solution of this problem. We also give a description of the spectrum for the corresponding operator.}, language = {en} } @unpublished{Tepoyan2000, author = {Tepoyan, Liparit}, title = {Degenerated operator equations of higher order}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25888}, year = {2000}, abstract = {Content: 1 Introduction 2 The one-dimensional case 2.1 The space Wm sub (α) 2.2 Self-adjoint Equation 2.3 Non-selfadjoint Equation 3 Operator Equation}, language = {en} } @article{MahmoudiSchulzeTepoyan2015, author = {Mahmoudi, Mahdi Hedayat and Schulze, Bert-Wolfgang and Tepoyan, Liparit}, title = {Continuous and variable branching asymptotics}, series = {Journal of pseudo-differential operators and applications}, volume = {6}, journal = {Journal of pseudo-differential operators and applications}, number = {1}, publisher = {Springer}, address = {Basel}, issn = {1662-9981}, doi = {10.1007/s11868-015-0110-3}, pages = {69 -- 112}, year = {2015}, abstract = {The regularity of solutions to elliptic equations on a manifold with singularities, say, an edge, can be formulated in terms of asymptotics in the distance variable r > 0 to the singularity. In simplest form such asymptotics turn to a meromorphic behaviour under applying the Mellin transform on the half-axis. Poles, multiplicity, and Laurent coefficients form a system of asymptotic data which depend on the specific operator. Moreover, these data may depend on the variable y along the edge. We then have y-dependent families of meromorphic functions with variable poles, jumping multiplicities and a discontinuous dependence of Laurent coefficients on y. We study here basic phenomena connected with such variable branching asymptotics, formulated in terms of variable continuous asymptotics with a y-wise discrete behaviour.}, language = {en} }