The Hodge star operator and the Beltrami equation

نویسندگان

چکیده

An essentially unique homeomorphic solution to the Beltrami equation with measurable coefficients was found in 1930s by Morrey. The most well-known proof from 1960s uses theory of Calderón–Zygmund and singular integral operators $$L^p(\mathbb {C})$$ . We will present an alternative method solve using Hodge star operator standard elliptic PDE theory. also discuss a different prove regularity solution. This approach is partially based on work Dittmar.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

The Hodge Star Operator

We’ll start out by defining the Hodge star operator as a map from ∧k(R) to ∧n−k(R). Here ∧k(R) denotes the vector space of alternating k-tensors on R. Later on, we will extend this definition to alternating tensors on a finite dimensional vector space that is equipped with an inner product. Let I = (i1, ..., ik) be some increasing multi-index of length k. That is i1 < i2 < i3 < .... Let J = (j1...

متن کامل

A Fermionic Hodge Star Operator

A fermionic analogue of the Hodge star operation is shown to have an explicit operator representation in models with fermions, in spacetimes of any dimension. This operator realizes a conjugation (pairing) not used explicitly in field-theory, and induces a metric in the space of wave-function(al)s just as in exterior calculus. If made real (Hermitian), this induced metric turns out to be identi...

متن کامل

The Hodge Dual Operator

The Hodge dual operator ∗ is one of the 3 basic operations on differential forms. (The other 2 are wedge product ∧ and exterior differentiation d.) However most treatments consider only positive-definite inner products, and there are at least 2 standard ways of generalizing this to inner products of arbitrary signature. We outline here a construction of the Hodge dual operator which works for a...

متن کامل

The Laplace-Beltrami-Operator on Riemannian Manifolds

This report mainly illustrates a way to compute the Laplace-Beltrami-Operator on a Riemannian Manifold and gives information to why and where it is used in the Analysis of 3D Shapes. After a brief introduction, an overview over the necessary properties of manifolds for calculating the Laplacian is given. Furthermore the two operators needed for defining the Laplace-Beltrami-Operator the gradien...

متن کامل

Image Processing via the Beltrami Operator

We present a framework for enhancing images while pre serving either the edge or the orientation dependent texture informa tion present in them We do this by treating images as manifolds in a feature space This geometrical interpretation leads to a natural way for grey level color movies volumetric medical data and color texture im age enhancement Following this we invoke the Polyakov action fr...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Complex analysis and its synergies

سال: 2022

ISSN: ['2197-120X', '2524-7581']

DOI: https://doi.org/10.1007/s40627-022-00096-1