相关论文: On integral conditions for the general Beltrami eq…

It is shown that many recent and new results on the existence of ACL homeomorphic (and more strong) solutions for the Beltrami equations with integral constraints follow from our extension of the well--known Lehto existence theorem.

It is established interconnections between various integral conditions that play an important role in the theory of space mappings and in the theory of degenerate Beltrami equations in the plane.

We construct variations for the classes of regular solutions to degenerate Beltrami equations with restrictions of the set-theoretic type for the complex coefficient. On this basis, we prove the variational maximum principle and other…

We establish a series of criteria on the existence of regular solutions for the Dirichlet problem to general degenerate Beltrami equations ${\bar{\partial}}f = \mu {\partial f}+\nu {\bar{\partial f}}$ in arbitrary Jordan domains in $\C$.

We study quasilinear Beltrami equations, the complex coefficients of which depend on the unknown function. In terms of the so-called tangential dilatation, we have found conditions under which these equations have homeomorphic…

Existence theorem is proven for the generating equations of the split involution constraint algebra. The structure of the general solution is established, and the characteristic arbitrariness in generating functions is described.

We consider problems concerning the existence of solutions of the Beltrami equations and their convergence in the entire complex plane. We are mainly interested in the case when these solutions satisfy the so-called hydrodynamic…

In two recent papers necessary and sufficient conditions for a given system of second-order ordinary differential equations to be of Lagrangian form with additional dissipative forces were derived. We point out that these conditions are not…

In this article, first we give a general lemma on the existence of regular homeomorphic solutions $f$ with the hydrodynamic normalization $f(z)=z+o(1)$ as $z\to\infty$ to the degenerate Beltrami equations $\overline{\partial}f=\mu\,\partial…

The article is devoted to questions concerning the problems of compactness of solutions of the Dirichlet problem for the Beltrami equation in some simply connected domain. In terms of prime ends, we have proved results of a detailed form…

In this work there is established an optimal existence and regularity theory for second order linear parabolic differential equations on a large class of noncompact Riemannian manifolds. Then it is shown that it provides a general unifying…

We have proved theorems on compact classes of homeomorphisms with hydrodynamic normalization that are solutions of the Beltrami equation, whose characteristics are compactly supported and satisfy certain constraints of an integral type. As…

A description of solutions of some integral equations has been obtained. A two-radii theorem is obtained as well.

We have found one of the possible conditions under which the Beltrami equation with degeneration of ellipticity has a continuous solution of the Sobolev class. With some additional requirements, this solution is homeomorphic

For the system of second order quasilinear parabolic equations the problem of reducing them to the equations of diffusion type is considered. In non-degenerate case an effective algorithm for solving this problem is suggested.

We present a new proof of a Finslerian version of Beltrami's theorem (1865) which works also in dimension 2.

The two main topics of this text are as follows: Firstly, three modifications of the theorem of Beltrami will be presented for diffeomorphisms between Riemannian manifolds and a space form which preserve the geodesic circles, the geodesic…

We study Beltrami-type equations with two given complex characteristics. Under certain conditions on the complex coefficients, we obtained theorems on the existence of homeomorphic $ ACL $ -solutions of this equation. In addition, for some…

We give sufficient conditions for the existence and uniqueness, in bounded uniformly convex domains $\Omega$, of solutions of degenerate elliptic equations depending also on the nonlinear gradient term $H$, in term of the size of $\Omega$,…

Elementary transformations of equations $A\psi=\lambda\psi$ are considered. The invertibility condition (Theorem 1) is established and similar transformations of Riccati equations in the case of second order differential operator $A$ are…