TY - INPR A1 - Ly, Ibrahim A1 - Tarkhanov, Nikolai Nikolaevich T1 - A Radó theorem for p-harmonic functions N2 - Let A be a nonlinear differential operator on an open set X in R^n and S a closed subset of X. Given a class F of functions in X, the set S is said to be removable for F relative to A if any weak solution of A (u) = 0 in the complement of S of class F satisfies this equation weakly in all of X. For the most extensively studied classes F we show conditions on S which guarantee that S is removable for F relative to A. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 4 (2015) 3 KW - Quasilinear equations KW - removable sets KW - p-Laplace Operator Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-71492 SN - 2193-6943 VL - 4 IS - 3 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - INPR A1 - Ly, Ibrahim A1 - Tarkhanov, Nikolai Nikolaevich T1 - Asymptotic expansions at nonsymmetric cuspidal points N2 - We study asymptotics of solutions to the Dirichlet problem in a domain whose boundary contains a nonsymmetric conical point. We establish a complete asymptotic expansion of solutions near the singular point. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 4 (2015) 7 KW - the Dirichlet problem KW - singular point KW - asymptotic expansion Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-78199 SN - 2193-6943 VL - 4 IS - 7 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - INPR A1 - Fedosov, Boris A1 - Tarkhanov, Nikolai Nikolaevich T1 - Deformation quantisation and boundary value problems N2 - We describe a natural construction of deformation quantisation on a compact symplectic manifold with boundary. On the algebra of quantum observables a trace functional is defined which as usual annihilates the commutators. This gives rise to an index as the trace of the unity element. We formulate the index theorem as a conjecture and examine it by the classical harmonic oscillator. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 4 (2015) 5 KW - symplectic manifold KW - star product KW - trace KW - index Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-77150 SN - 2193-6943 VL - 4 IS - 5 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - INPR A1 - Elin, Mark A1 - Shoikhet, David A1 - Tarkhanov, Nikolai Nikolaevich T1 - Analytic semigroups of holomorphic mappings and composition operators N2 - In this paper we study the problem of analytic extension in parameter for a semigroup of holomorphic self-mappings of the unit ball in a complex Banach space and its relation to the linear continuous semigroup of composition operators. We also provide a brief review around this topic. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 4 (2015) 6 KW - nonlinear semigroup KW - composition operator Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-77914 SN - 2193-6943 VL - 4 IS - 6 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - INPR A1 - Alsaedy, Ammar A1 - Tarkhanov, Nikolai Nikolaevich T1 - Weak boundary values of solutions of Lagrangian problems N2 - We define weak boundary values of solutions to those nonlinear differential equations which appear as Euler-Lagrange equations of variational problems. As a result we initiate the theory of Lagrangian boundary value problems in spaces of appropriate smoothness. We also analyse if the concept of mapping degree of current importance applies to the study of Lagrangian problems. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 4 (2015) 2 KW - nonlinear equations KW - Lagrangian system KW - weak boundary values KW - quasilinear Fredholm operator KW - mapping degree Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-72617 SN - 2193-6943 VL - 4 IS - 2 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - INPR A1 - Tarkhanov, Nikolai Nikolaevich T1 - A spectral theorem for deformation quantisation N2 - We present a construction of the eigenstate at a noncritical level of the Hamiltonian function. Moreover, we evaluate the contributions of Morse critical points to the spectral decomposition. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 4 (2015) 4 KW - star product KW - WKB method KW - spectral theorem Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-72425 SN - 2193-6943 VL - 4 IS - 4 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - INPR A1 - Makhmudov, K. O. A1 - Makhmudov, O. I. A1 - Tarkhanov, Nikolai Nikolaevich T1 - A nonstandard Cauchy problem for the heat equation N2 - We consider a Cauchy problem for the heat equation in a cylinder X x (0,T) over a domain X in the n-dimensional space with data on a strip lying on the lateral surface. The strip is of the form S x (0,T), where S is an open subset of the boundary of X. The problem is ill-posed. Under natural restrictions on the configuration of S we derive an explicit formula for solutions of this problem. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 4 (2015)11 KW - heat equation KW - Cauchy problem KW - Carleman formulas Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-83830 SN - 2193-6943 VL - 4 IS - 11 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - INPR A1 - Mera, Azal A1 - Shlapunov, Alexander A1 - Tarkhanov, Nikolai Nikolaevich T1 - Navier-Stokes equations for elliptic complexes N2 - We continue our study of invariant forms of the classical equations of mathematical physics, such as the Maxwell equations or the Lamé 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. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 4 (2015)12 KW - Navier-Stokes equations KW - classical solution Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-85592 SN - 2193-6943 VL - 4 IS - 12 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - INPR A1 - Gibali, Aviv A1 - Shoikhet, David A1 - Tarkhanov, Nikolai Nikolaevich T1 - On the convergence of continuous Newton method N2 - In this paper we study the convergence of continuous Newton method for solving nonlinear equations with holomorphic mappings in complex Banach spaces. Our contribution is based on a recent progress in the geometric theory of spirallike functions. We prove convergence theorems and illustrate them by numerical simulations. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 4 (2015)10 KW - Newton method KW - spirallike function Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-81537 SN - 2193-6943 VL - 4 IS - 10 PB - Universitätsverlag Potsdam CY - Potsdam ER -