E. A. Sevost'yanov
We study mappings satisfying the so-called inverse Poletsky inequality. Under integrability of the corresponding majorant, it is proved that these mappings are logarithmic Hölder continuous in the neighborhood of the boundary points. In particular, the indicated properties hold for homeomorphisms whose inverse satisfy the weighted Poletsky inequality.
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In this article, we consider the Hölder continuity of injective maps in Orlicz-Sobolev classes defined on the unit ball. Under certain conditions on the growth of dilatations, we obtain the Hölder continuity of the indicated class of mappings. In particular, under certain special restrictions, we show that Lipschitz continuity of mappings holds. We also consider Hölder and Lipschitz continuity of harmonic mappings and in particular of harmonic mappings in Orlicz-Sobolev classes. In addition in planar case, we show in some situations that the map is bi-Lipschitzian if Beltrami coefficient is Hö…
It is founded the sufficient condition of Holder continuity of the ring $Q$-homeomorphisms in $\mathbb{R}^n, n\geq 2$ with respect to $p$-modulus at $n-1<p<n$.
We study mappings with branching of a domain of Euclidean space. The Hölder and Lipschitz continuity are established for one class of spatial mappings whose characteristic satisfies the Dini type condition in a given domain. In addition, we found conditions on the complex coefficient of the degenerate Beltrami equations in the unit disk under which generalized homeomorphic solutions of this equation are Hölder continuous at the points of the boundary.
We prove that for harmonic quasiconformal mappings $α$-Hölder continuity on the boundary implies $α$-Hölder continuity of the map itself. Our result holds for the class of uniformly perfect bounded domains, in fact we can allow that a portion of the boundary is thin in the sense of capacity. The problem for general bounded domains remains open.
On boundary Hölder logarithmic continuity of mappings in some domains
本文研究了满足路径族模畸变估计的映射，证明了在定义域和映射区域满足特定条件时，这些映射在边界点具有对数 Hölder 连续性。
We establish that every $K$-quasiconformal mapping $w$ of the unit ball $\IB$ onto a $C^2$-Jordan domain $Ω$ is Hölder continuous with constant $α= 2-\frac{n}{p}$, provided that its weak Laplacean $Δw$ is in $ L^p(\IB)$ for some $n/2<p<n$. In particular it is Hölder continuous for every $0<α<1$ provided that $Δw\in L^n(\IB)$.
Hilbert metric and Hölder continuity of quasiregular mappings
本文研究了单位圆盘到有界凸域的准共形映射的Hölder连续性，基于Hilbert度量，并提出了若干开放问题。
Let V_E be the pluricomplex Green function associated to a compact subset E of C^N. The well known Hölder Continuity Property of E means that there exist constants B > 0, 0< c =< 1 such that V_E(z) =< B dist(z,E)^c. The main result of this paper says that this condition is equivalent to a Vladimir Markov type inequality, i.e. || D^αP ||_E =< M^{|α|} (deg P)^{m|α|} (|α|!)^{1-m} ||P||_E, where m,M>0 are independent of the polynomial P of N variables. We give some applications of this equivalence and we present its generalization related to a notion of a fit majorant. Moreover, as a consequence o…
On boundary Hölder continuity of mappings with the Poletsky condition
本文研究了满足 Poletsky 不等式扭曲路径族模数的映射，在特征具有有限积分平均的条件下，证明了其在同胚与分支映射、良好边界与素端边界情形下的边界 Hölder 连续性。
The paper is devoted to the study of mappings satisfying the inverse Poletsky inequality. We study the local behavior of these mappings, moreover, we are most interested in the case when the corresponding majorant is integrable on some set of spheres of positive linear measure. The most important result is a logarithmic Hölder continuity of such mappings at inner points. As a corollary, we obtained the existence of a continuous $ACL$-solution of the Beltrami equation, which is logarithmic Hölder continuous.
On boundary Hölder continuity of Sobolev and Orlicz-Sobolev classes
研究映射在领域边界点处的扭曲估计，探讨Sobolev和Orlicz-Sobolev类及其他不保持边界映射的性质，证明在特定条件下映射的Hölder连续性。
We study Hölder continuity of solutions to the Monge-Ampère equations on compact Kähler manifolds. In [DNS] the authors have shown that the measure $ω_u^n$ is moderate if $u$ is Hölder continuous. We prove a theorem which is a partial converse to this result.
We show that a $K$-quasiregular $ω$-curve from a Euclidean domain to a Euclidean space with respect to a covector $ω$ is locally $(1/K)(\lVert ω\rVert/|ω|_{\ell_1})$-Hölder continuous. We also show that quasiregular curves enjoy higher integrability.
Hölder continuity and composition operators in pluriharmonic Bloch spaces
该研究针对复空间单位球上的多调和Bloch映射，证明了对应于Bergman度量的Hölder估计，进而得到多调和Bloch空间复合算子下方有界的充分条件及全纯映射Bloch空间复合算子下方有界的必要条件。
We consider the Dirichlet problem for the complex Monge-Ampère equation in a bounded strongly hyperconvex Lipschitz domain in $\C^n$. We first give a sharp estimate on the modulus of continuity of the solution when the boundary data is continuous and the right hand side has a continuous density. Then we consider the case when the boundary value function is $C^{1,1}$ and the right hand side has a density in $L^p(Ω)$ for some $p>1$ and prove the Hölder continuity of the solution.
We prove the continuity of logarithmic capacity under Hausdorff convergence of uniformly perfect planar sets. The continuity holds when the Hausdorff distance to the limit set tends to zero at sufficiently rapid rate, compared to the decay of the parameters involved in the uniformly perfect condition. The continuity may fail otherwise.
Hölder continuity and laminarity of the Green currents for Hénon-like maps
研究Hénon-like映射的Green流的Hölder连续超势及层性，证明其最大熵测度为Monge-Ampère流，并具有正Hausdorff维数。
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