# Tagged Questions

30 views

### Does this integral equation have a name, and is there a reference that deals with it?

The equation is $$S(z,t)=\int_a^b \int_c^d f(z,u) g(t,s) S(u,s) \, du \, ds$$ where $S$ is the unknown function and $f,\ g$ are fixed from the outset. I can approximate solutions in some special ...
27 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 ...
28 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 ...
31 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 $K(z,w)$ ...
56 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 ...