Related papers: On Bloch's Theorem for Heat Maps

We study the existence and uniqueness of source-type solutions to the Cauchy problem for the heat equation with fast convection under certain tail control assumptions. We allow the solutions to change sign, but we will in fact show that…

A branch of generalizations of the Banach Fixed Point Theorem replaces contractivity by a weaker but still effective property. The aim of the present note is to extend the contraction principle in this spirit for such complete semimetric…

Let $p:\mathbb{C}\to\mathbb{R}$ be a subharmonic, nonharmonic polynomial and $\tau$ a real parameter. Define $\bar{Z}_{\tau p} = \partial_{\bar z} + \tau p_{\bar z}$, a closed, densely-defined operator on $L^2(\mathbb{C})$. If $\Box_{\tau…

The Hall-Vinen-Bekharevich-Khalatnikov (HVBK) equations are a macroscopic model of superfluidity at non-zero temperatures. For smooth, compactly supported data, we prove the global well-posedness of strong solutions to these equations in…

Polterovich proved a remarkable closed formula for heat kernel coefficients of the Laplace operator on compact Riemannian manifolds involving powers of Laplacians acting on the distance function. In the case of K\"ahler manifolds, we prove…

The article deals with the generalized Newton--Kantorovich method for solving operator equations with nondifferentiable operators in Banach spaces. The convergence theorem is proved by means of majorant scalar equations.

We establish Lipschitz regularity of harmonic maps from $\mathrm{RCD}(K,N)$ metric measure spaces with lower Ricci curvature bounds and dimension upper bounds in synthetic sense with values into $\mathrm{CAT}(0)$ metric spaces with…

The Cauchy problem for the linearization of a system of equations arising in the kinetic theory of a condensed gas of bosons near the critical temperature around one of its equilibria is solved for radially symmetric initial data. It is…

We established a fixed-point theorem for mapping satisfying a general contractive inequality of integral type depended an another function. This theorem substantially extend the theorem due to Branciari (2003) and Rhoades (2003)

In this paper, we first obtain an estimate of the coefficients for $\alpha$-harmonic mappings. By applying these coefficient estimates, we prove the Landau type theorem for $\alpha$-harmonic mappings defined on the unit disc $\ID$.

We derive closed formula for the heat kernel $K_\mathbb{H}$ associated to Maass-Laplacian operator $D_k$ for any real $k$ and prove that heat kernel $K_\mathbb{H}$ is strictly monotone decreasing function. We also derive some important…

In this study, we establish certain Landau-type theorems for functions with logharmonic Laplacian of the form $F(z)=|z|^2L(z)+K(z)$, $|z|<1$, where $L$ is logharmonic and $K$ is harmonic, with $L$ and $K$ having bounded length distortion in…

We show the existence of smooth stationary solutions for the inelastic Boltzmann equation under the thermalization induced by a host-medium with a fixed distribution. This is achieved by controlling the Lp-norms, the moments and the…

A version of the classical Klee-And\^o Theorem states the following: For every Banach space $X$, ordered by a closed generating cone $C\subseteq X$, there exists some $\alpha>0$ so that, for every $x\in X$, there exist $x^{\pm}\in C$ so…

Let $M$ be a $C^{2}$-smooth Riemannian surface. A classical theorem in differential geometry states that the Gauss curvature function $K : M \to \mathbb{R}$ vanishes everywhere if and only if the surface is locally isometric to the…

We proved an Liouville theorem for Backward V T-harmonic map heat flow from evolution manifolds into generalized regular ball. Among others, we also proved an Liouville theorem for V T-harmonic map heat flow from complete manifolds into…

In this paper we show how using a relativistic kinetic equation the ensuing expression for the heat flux can be casted in the form required by Classical Irreversible Thermodynamics. Indeed, it is linearly related to the temperature and…

In this paper, we show that several extension of Banach contraction principle, can be easily derived from the Caristi's theorem is one of the useful generalization of Banach contraction principle in the setting of the complete metric…

The aim of this note is to give a simplified proof of the surjectivity of the natural Milnor-Chow homomorphism $\rho: K^M_n(A) \to CH^n(A,n)$ between Milnor $K$-theory and higher Chow groups for essentially smooth (semi-)local $k$-algebras…

We present closed graph and open mapping theorems for $\wt{\C}$-linear maps acting between suitable classes of topological and locally convex topological $\wt{\C}$-modules. This is done by adaptation of De Wilde's theory of webbed spaces…