Integration by parts for nonsymmetric fractional-order operators on a halfspace

نویسندگان

چکیده

For a strongly elliptic pseudodifferential operator $L$ of order $2a$ ($00$. Here deduce "halfways Green's formula" $L$: $$ \int_{R^n_+} Lu\,\bar v\,dx-\int_{R^n_+}u\,\overline{ L^*v}\,dx=c\int_{R^{n-1}}\gamma_0(u/x_n^{\mu -1 })\,{\gamma_0(\bar v/x_n^{\mu ^*})}\, dx', $u$ solves problem $L$, $v$ $L^*$; ^*=2a-\mu $. Finally, full formula, solve problems; here Neumann traces enter, as well first-order over boundary.

برای دانلود رایگان 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

Local Integration by Parts and Pohozaev Identities for Higher Order Fractional Laplacians

We establish an integration by parts formula in bounded domains for the higher order fractional Laplacian (−∆) with s > 1. We also obtain the Pohozaev identity for this operator. Both identities involve local boundary terms, and they extend the identities obtained by the authors in the case s ∈ (0, 1). As an immediate consequence of these results, we obtain a unique continuation property for th...

متن کامل

Summation-by-parts operators and high-order quadrature

Summation-by-parts (SBP) operators are finite-difference operators that mimic integration by parts. The SBP operator definition includes a weight matrix that is used formally for discrete integration; however, the accuracy of the weight matrix as a quadrature rule is not explicitly part of the SBP definition. We show that SBP weight matrices are related to trapezoid rules with end corrections w...

متن کامل

On Coordinate Transformations for Summation-by-Parts Operators

High order finite difference methods obeying a summation-by-parts (SBP) rule are developed for equidistant grids. With curvilinear grids, a coordinate transformation operator that does not destroy the SBP property must be used. We show that it is impossible to construct such an operator without decreasing the order of accuracy of the method.

متن کامل

Integration by parts

Integration by parts is used to reduce scalar Feynman integrals to master integrals.

متن کامل

Feynman Diagrams and a Combination of the Integration by Parts (IBP) and the Integration by Fractional Expansion (IBFE) Techniques

In this paper we show how to improve and extend the Integration by Fractional Expansion technique (IBFE) by applying it to certain families of scalar massive Feynman diagrams. The strategy is based on combining this method together with the Integration by Parts technique (IBP). In particular, we want to calculate certain Feynman diagrams which have a triangle loop as a subgraph. The main idea i...

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: Journal of Mathematical Analysis and Applications

سال: 2021

ISSN: ['0022-247X', '1096-0813']

DOI: https://doi.org/10.1016/j.jmaa.2021.125012