Results 91 to 100 of about 1,270,291 (205)

The Loewner–Kufarev energy and foliations by Weil–Petersson quasicircles

Proceedings of the London Mathematical Society, Volume 128, Issue 2, February 2024.
Abstract We study foliations by chord–arc Jordan curves of the twice punctured Riemann sphere C∖{0}$\mathbb {C} \setminus \lbrace 0\rbrace$ using the Loewner–Kufarev equation. We associate to such a foliation a function on the plane that describes the “local winding” along each leaf. Our main theorem is that this function has finite Dirichlet energy if
Fredrik Viklund, Yilin Wang
wiley   +1 more source

Mappings of generalized finite distortion and continuity

Journal of the London Mathematical Society, Volume 109, Issue 1, January 2024.
Abstract We study continuity properties of Sobolev mappings f∈Wloc1,n(Ω,Rn)$f \in W_{\mathrm{loc}}^{1,n} (\Omega , \mathbb {R}^n)$, n⩾2$n \geqslant 2$, that satisfy the following generalized finite distortion inequality Df(x)n⩽K(x)Jf(x)+Σ(x)$$\begin{equation*} \hspace*{4.6pc}{\left| Df(x) \right|}^n \leqslant K(x) J_f(x) + \Sigma (x) \end{equation ...
Anna Doležalová, Ilmari Kangasniemi, Jani Onninen   +2 more
wiley   +1 more source

Semilinear equations in a plane and quasiconformal mappings

Доповiдi Нацiональної академiї наук України
We consider generalizations of the Bieberbach equation with nonlinear right parts, which makes it possible to study many problems of mathematical physics in inhomogeneous and anisotropic media with smooth characteristics.
V.Ya. Gutlyanskiĭ, O.V. Nesmelova, V.I. Ryazanov   +2 more
doaj   +1 more source

On the boundary behavior of weak (p; q)-quasiconformal mappings

Journal of Mathematical Sciences, 2023
V. Gol’dshtein, E. Sevost’yanov, A. Ukhlov   +2 more
semanticscholar   +1 more source

On blow-up solutions and dead zones in semilinear equations

Доповiдi Нацiональної академiї наук України
Presented by Corresponding Member of the NAS of Ukraine V.Ya. Gutlyanskii We study semilinear elliptic equations of the form div(A(z)∇u)=f(u) in Ω⊂C, where A(z) stands for a sym metric 2×2 matrix function with measurable entries, detA=1, and such that 1/
V.Ya. Gutlyanskiĭ, O.V. Nesmelova, V.I. Ryazanov   +2 more
doaj   +1 more source

Isometries for the modulus metric are quasiconformal mappings

Transactions of the American Mathematical Society, 2017
For a domain D D in R ¯ n \bar {\mathbb R}^n , the modulus metric is defined by μ D (
Dimitrios Betsakos, S. Pouliasis
semanticscholar   +1 more source

Semilinear equations in the plane with measurable data

Доповiдi Нацiональної академiї наук України
We study semilinear partial differential equations in the plane, the linear part of which is written in a divergence form. The main result is given as a factorization theorem.
V.Ya. Gutlyanskiĭ, O.V. Nesmelova, V.I. Ryazanov   +2 more
doaj   +1 more source

Quasiconformal Extensions of Harmonic Mappings

The Journal of Geometric Analysis, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +3 more sources

Identification of the Coordinates of Impulse Pollution Sources in Anisotropic Environments using Numerical Quasiconformal Mapping Methods

Journal of Optimization, Differential Equations and Their Applications
A combined approach to identifying the coordinates of point impulse sources, using observation data at certain time intervals at characteristic points, has been transferred to the case of anisotropy.
Andrii Y. Bomba, Mykhailo V. Boichura, Nataliia V. Ivanchuk   +2 more
doaj   +1 more source

Extremal Problems for Quasiconformal Mappings

Journal of Mathematical Analysis and Applications, 2000
Let \(X\) and \(Y\) be two hyperbolic Riemann surfaces covered by the unit disc \(\Delta=\{z;|z|
openaire   +2 more sources