TY  - INPR
A1  - Shlapunov, Alexander
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Golusin-Krylov Formulas in Complex Analysis
T2  - Preprints des Instituts für Mathematik der Universität Potsdam
N2  - This is a brief survey of a constructive technique of analytic continuation related to an explicit integral formula of Golusin and Krylov (1933). It goes far beyond complex analysis and applies to the Cauchy problem for elliptic partial differential equations as well. As started in the classical papers, the technique is elaborated in generalised Hardy spaces also called Hardy-Smirnov spaces.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 6 (2017) 2 
KW  - analytic continuation
KW  - integral formulas
KW  - Cauchy problem
Y1  - 2017
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-102774
VL  - 6
IS  - 2
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Alsaedy, Ammar
T1  - Variational primitive of a differential form
N2  - In this paper we specify the Dirichlet to Neumann operator related to the Cauchy problem for the gradient operator with data on a part of the boundary. To this end, we consider a nonlinear relaxation of this problem which is a mixed boundary problem of Zaremba type for the p-Laplace equation.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 5 (2016) 4 
KW  - Dirichlet-to-Neumann operator
KW  - Cauchy problem
KW  - p-Laplace operator
KW  - calculus of variations
Y1  - 2016
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-89223
SN  - 2193-6943
VL  - 5
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  -