1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Integral equation

  1. Jan 18, 2010 #1
    1. The problem statement, all variables and given/known data

    If we want to show whether a kernel is weakly singular or not, what do we do?

    eg. consider:

    a) [tex]\int_0^x sin(x-s)y(s)ds[/tex]

    b) [tex]\int_{-3}^3 \frac{y(s)}{x-s}ds[/tex]

    2. Relevant equations

    A discontinuous kernel k(x; s) is weakly singular (at x = s) if k is continu-
    ous when x [tex]\neq[/tex] s and if [tex]\exists[/tex] constants v[tex]\in[/tex] (0; 1) and c > 0 such that [tex]\left|k(x,s)\right|\leq c \left|x-s\right|^{-v}[/tex] for x [tex]\neq[/tex] s on its set of defnition.

    3. The attempt at a solution

    a) I dont think this is weakly singular because when x=s, the kernel is continuous.

    b) when x=s, the kernel is discontinuous because the equation tends to infinity. and we can say that v=1/2 and c=1.

    I feel like this is wrong. but even if it's right, i think it lacks explanation
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted