307 research outputs found
Multidimensional Inverse and Ill-Posed Problems for Differential Equations
This monograph is devoted to statements of multidimensional inverse problems, in particular to methods of their investigation. Questions of the uniqueness of solution, solvability and stability are studied. Methods to construct a solution are given and, in certain cases, inversion formulas are given as well. Concrete applications of the theory developed here are also given. Where possible, the author has stopped to consider the method of investigation of the problems, thereby sometimes losing generality and quantity of the problems, which can be examined by such a method. The book should be of interest to researchers in the field of applied mathematics, geophysics and mathematical biology
Asymptotic invariants, complexity of groups and related problems
We survey results about computational complexity of the word problem in
groups, Dehn functions of groups and related problems.Comment: 86 pages. Preliminary version, comments are welcome. v2: some
references added, misprints fixed, some changes suggested by the readers are
made. 88 pages. v3: more readers' suggestions implemented, index added, the
list of references improved. This version is submitted to a journal. v4: The
paper is accepted in Bulletin of Mathematical Science
Hypersurfaces of prescribed curvature in hyperbolic space
In this paper we consider the problem of existence of hypersurfaces with prescribed curvature in hyperbolic space. We use the upper half-space model of hyperbolic space. The hypersurfaces we consider are given as graphs of positive functions on some domain Ω ∈ Rn satisfying equations of form
f (A) = f (κ1, . . . , κn) = ψ,
where A is the second fundamental form of a hypersurface, f (A) is a smooth sym- metric function of the eigenvalues of A and ψ is a function of position. If we impose certain conditions on f and ψ, the above equation can be treated as an elliptic, fully non-linear partial differential equation
G(D2u, Du, u) = ψ(x, u).
We then derive an existence result for the corresponding Dirichlet problem
- …