Remarks on the Gauss-Green Theorem
نویسنده
چکیده
These notes cover material related to the Gauss-Green theorem that was developed for work with S. Hofmann and M. Mitrea, which appeared in [HMT].
منابع مشابه
Introduction to Calculus in Several Variables
1 2 Contents 0. One-variable calculus 1. The derivative 2. Inverse function and implicit function theorem 3. Fundamental local existence theorem for ODE 4. The Riemann integral in n variables 5. Integration on surfaces 6. Differential forms 7. Products and exterior derivatives of forms 8. The general Stokes formula 9. The classical Gauss, Green, and Stokes formulas 10. Holomorphic functions and...
متن کاملRemarks on the Paper ``Coupled Fixed Point Theorems for Single-Valued Operators in b-Metric Spaces''
In this paper, we improve some recent coupled fixed point resultsfor single-valued operators in the framework of ordered $b$-metricspaces established by Bota et al. [M-F. Bota, A. Petrusel, G.Petrusel and B. Samet, Coupled fixed point theorems forsingle-valued operators in b-metric spaces, Fixed Point TheoryAppl. (2015) 2015:231]. Also, we prove that Perov-type fix...
متن کاملON AN EXTENSION OF A QUADRATIC TRANSFORMATION FORMULA DUE TO GAUSS
The aim of this research note is to prove the following new transformation formula begin{equation*} (1-x)^{-2a},_{3}F_{2}left[begin{array}{ccccc} a, & a+frac{1}{2}, & d+1 & & \ & & & ; & -frac{4x}{(1-x)^{2}} \ & c+1, & d & & end{array}right] \ =,_{4}F_{3}left[begin{array}{cccccc} 2a, & 2a-c, & a-A+1, & a+A+1 & & \ & & & & ; & -x \ & c+1, & a-A, & a+A & & end{array} right], end{equation*} wher...
متن کاملL_1 operator and Gauss map of quadric surfaces
The quadrics are all surfaces that can be expressed as a second degree polynomialin x, y and z. We study the Gauss map G of quadric surfaces in the 3-dimensional Euclidean space R^3 with respect to the so called L_1 operator ( Cheng-Yau operator □) acting on the smooth functions defined on the surfaces. For any smooth functions f defined on the surfaces, L_f=tr(P_1o hessf), where P_1 is t...
متن کاملGauss-green Theorem for Weakly Differentiable Vector Fields, Sets of Finite Perimeter, and Balance Laws
We analyze a class of weakly differentiable vector fields F : R → R with the property that F ∈ L∞ and div F is a Radon measure. These fields are called bounded divergencemeasure fields. The primary focus of our investigation is to introduce a suitable notion of the normal trace of any divergence-measure field F over the boundary of an arbitrary set of finite perimeter, which ensures the validit...
متن کامل