We know the following associations :
- Volterra Integral Equations $\leftrightarrow$ Initial Value Problems
- Fredholm Integral Equations $\leftrightarrow$ Boundary Value Problems
My questions are :
- Can we associate a partial differential equation with an integral equation, ie can we convert a partial differential equation to an integral equation and vice-versa ?
- Can every integral equation be converted to a differential equation ? I have this doubt because the space of integrable functions is much bigger than the space of differentiable functions as we know that continuity is not necessary for integration.