@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} } @book{Tepoyan2000, author = {Tepoyan, Liparit}, title = {Degenerated operator equations og higher order}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {13 S.}, year = {2000}, language = {en} } @book{Tepoyan2004, author = {Tepoyan, Liparit}, title = {The Neumann problem for a degenerate operator equation}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {11 S.}, year = {2004}, language = {en} } @book{Tepoyan2008, author = {Tepoyan, Liparit}, title = {The Mixed problem for a degenerate operator equation}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {13 S.}, year = {2008}, language = {en} }