Tarantello G.'s An Harnak inequality for Liouville-type equations with PDF

By Tarantello G.

Show description

Read Online or Download An Harnak inequality for Liouville-type equations with singular sources PDF

Best mathematics books

Download e-book for iPad: Ellipsoidal Harmonics: Theory and Applications (Encyclopedia by George Dassios

The field is what will be referred to as an ideal form. regrettably, nature is imperfect and lots of our bodies are higher represented by way of an ellipsoid.

The conception of ellipsoidal harmonics, originated within the 19th century, may possibly merely be heavily utilized with the type of computational energy to be had lately. This, accordingly, is the 1st ebook dedicated to ellipsoidal harmonics. themes are drawn from geometry, physics, biosciences and inverse difficulties.

It includes classical effects in addition to new fabric, together with ellipsoidal biharmonic services, the speculation of pictures in ellipsoidal geometry, and vector floor ellipsoidal harmonics, which express a fascinating analytical constitution. prolonged appendices supply every little thing one must clear up officially boundary worth difficulties. End-of-chapter difficulties supplement the idea and try out the reader s knowing.

The e-book serves as a accomplished reference for utilized mathematicians, physicists, engineers, and for somebody who must recognize the present cutting-edge during this attention-grabbing topic. "

Download PDF by Pavel Etingof, Frederic Latour: The Dynamical Yang-Baxter Equation, Representation Theory,

The textual content relies on a longtime graduate direction given at MIT that gives an advent to the idea of the dynamical Yang-Baxter equation and its functions, that is an incredible quarter in illustration idea and quantum teams. The e-book, which incorporates many specified proofs and particular calculations, could be available to graduate scholars of arithmetic, who're accustomed to the fundamentals of illustration idea of semi-simple Lie algebras.

Additional info for An Harnak inequality for Liouville-type equations with singular sources

Sample text

3 Boundary Problem problem, we show how these unknowns are calculated. To make things simple, we assume that no charges are distributed on the plane. The problem under consideration examines in a section of a disk in which boundaries have fixed potential values FHr, j = 0L = 0, FHr, j = aL = 0, and FHr = R, jL = F0 Hj L. 5. 5. R FHr,j=0L=0 Boundary conditions on a disk segment. The domain G is free of charges. The domain G is free of any charges and the potential FHr, jL is regular and finite for r Ø 0.

5 Exercises 1. Create some pictures for a quadrupole arrangement of charges using the package PointCharge'. Choose the location of the charges in the representation plane of the potential section. What changes are required if your choice of coordinates for the charges is outside the representation plane? Perform some experiments with a larger number of charges. 2. , F0 = sin(j) or F0 = j). What changes occur in the potential if we change the angle a? Examine the influence of the upper summation index N on the accuracy of the solution.

As a consequence, we get n = n p ê a with n = 0, 1, 2, 3, ... The angular part of the solution thus reduces to np hn HjL = An sin H ÅÅÅÅaÅÅÅÅ jL. 41) that bn = 0. 42) where dn = an An . 3 Boundary Problem representations. Values for dn are determined by applying the boundary condition on the circle FHr = R, jL = F0 HjL. 44) or in explicit form, 2 a np Å F HjL sinH ÅÅÅÅaÅÅÅÅ jL d j. 45) includes the boundary condition and only contains known parameters. Thus, we can determine dn 's numerical value if we know the boundary condition and if we specify the index m of the expansion in Eq.

Download PDF sample

An Harnak inequality for Liouville-type equations with singular sources by Tarantello G.


by Mark
4.5

Rated 4.98 of 5 – based on 13 votes