Related papers: Beltrami equation for the harmonic diffeomorphisms…
In this paper we prove some results on the boundary behavior of solutions to fractional elliptic problems. Firstly, we establish a Hopf Lemma for solutions to some integro-differential equations. The main novelty of our result is that we do…
In the present paper we consider two related problems, i.e. the description of geodesics and the calculation of the spectrum of the Laplace-Beltrami operator on a flag manifold. We show that there exists a family of invariant metrics such…
We study fully nonlinear elliptic equations on Hermitian manifolds through blow-up argument and partial uniform ellipticity. We apply our results to draw geometric conclusions on finding conformal Hermitian metrics with prescribed…
Recently, the authors of this paper introduced logarithmic Hochschild (co)homology of logarithmic spaces in a geometric way using formality of derived intersections. In this paper, the authors extend the decomposition theorem for the…
A finite-area holomorphic quadratic differentials on an arbitrary Riemann surface $X=\mathbb{H}/\Gamma$ is uniquely determined by its horizontal measured foliation. By extending our prior result for $\Gamma$ of the first kind to arbitrary…
We prove a number of results on the interrelation between the $L^p$-metric on the group of Hamiltonian diffeomorphisms of surfaces and the subset of all autonomous Hamiltonian diffeomorphisms. More precisely, we show that there are…
We emphasize that construction of travelling wave solutions for partial differential equations is a problem of considerable interest and thus introduce a simple algebraic method to generate such solutions for equations in the Burgers…
In this paper we prove an isoperimetric inequality for holomorphic functions in the unit polydisc $\mathbf U^n$. As a corollary we derive an inclusion relation between weighted Bergman and Hardy spaces of holomorphic functions in the…
In this short article, we state a Hopf type lemma for fractional equations and the outline of its proof. We believe that it will become a powerful tool in applying the method of moving planes on fractional equations to obtain qualitative…
We estimate the linear isoperimetric constants of an n-dimensional ellipse. Using these estimates and a technique of Gromov, we estimate the Hopf and linking invariants of Lipschitz maps from ellipses to round spheres. Using these…
This paper is concerned with nonlinear elliptic equations in nondivergence form where the operator has a first order drift term which is not Lipschitz continuous. Under this condition the equations are nonhomogeneous and nonnegative…
Connected branches of periodic orbits originating at a Hopf bifurcation point of a differential system are considered. A computable estimate for the range of amplitudes of periodic orbits contained in the branch is provided under the…
The aim of this paper is to establish properties of the solutions to the $\alpha$-harmonic equations: $\Delta_{\alpha}(f(z))=\partial{z}[(1-{|{z}|}^{2})^{-\alpha} \overline{\partial}{z}f](z)=g(z)$, where…
An effective algorithm is presented for solving the Beltrami equation fzbar = mu fz in a planar disk. The algorithm involves no evaluation of singular integrals. The strategy, working in concentric rings, is to construct a piecewise linear…
We discuss a numerical algorithm for solving nonlinear integro-differential equations, and illustrate our findings for the particular case of Volterra type equations. The algorithm combines a perturbation approach meant to render a…
We show some of the mathematics that is being developed for the computation of deep inelastic structure functions to three loops. These include harmonic sums, harmonic polylogarithms and a class of difference equations that can be solved…
Let X be a Riemannian symmetric space of non-compact type. We prove a theorem of holomorphic extension for eigenfunctions of the Laplace-Beltrami operator on X, by techniques from the theory of partial differential equations.
In this paper we established the condition for a curve to satisfy stochas- tic fractional HP (Hamilton-Pontryagin) equations. These equations are described using It^o integral. We have also considered the case of stochastic fractional…
We present a method for explicit leapfrog integration of inseparable Hamiltonian systems by means of an extended phase space. A suitably defined new Hamiltonian on the extended phase space leads to equations of motion that can be…
The first author's geometric Hopf invariant of a stable map $F:\Sigma^{\infty}X \to \Sigma^{\infty}Y$ is a stable ${\mathbb Z}_2$-equivariant map $h(F):\Sigma^{\infty}X \to \Sigma^{\infty}(Y \wedge Y)$ constructed by an explicit difference…