1
vote
0answers
23 views

Smoothness of solutions to Fredholm integral equation

Let $K(x,y)=k(|x-y|)$ where $k$ is continuous on $(0,1]$, and assume function $f\in L^2[0,1]$ satisfies $f(x)=\int_0^1 f(y)K(x,y)dy$. Is $f$ necessarily $C^\infty $ ? under what condition on kernel ...
0
votes
1answer
27 views

Analyticity of Logarithmic Integrals

Assume $f\in L^2[0,1]$ and let $g(x)=\int_0^1f(y)\ln|x-y|dy$. Is it true that $g\in C^\infty(0,1)$? Is it true that $g$ is analytic in $(0,1)$? Can you refer me to a right reference to look up such ...
0
votes
0answers
28 views

Regulairty of eigenfunctions of singular integral equations

Can you provide a proof or a reference, to study from, for the following problem: Let $\Gamma$ be a real analytic rectifiable closed curve in the plane, $ds$ is the arc-length , and kernel $K(z,w)$ ...
2
votes
0answers
47 views

reference request: a graduate level textbook on viscosity solutions of IPDEs

I am particularly interested in IPDE which arises from optimal stopping/control problems so I would like some references on integral-partial differential equations, which are related this area. I have ...
6
votes
2answers
227 views

A nonlinear “Fredholm” integral equation

Consider the integral equation \begin{eqnarray*} u \left( x \right) & = & \int_0^{\infty} u \left( t \right) u \left( \frac{x}{t} \right) \mathrm{d} t \end{eqnarray*} where the objective ...
0
votes
1answer
79 views

Symbolic manipulations of integral equations

I was trying to learn about solving integral equations using symbolic algorithms. After a quick web search, I mostly found items like this Mathematica journal article that mostly focuses on how to use ...