Consider a parabolic problem PDE, on a domain, say $(0,T)\times (x_1,x_2)$ Let's say we have $Lu(x,t) = f(x,t;p)$ with boundary conditions $u(x_1,t)=g_1(t;p)$, $u(x_2,t)=g_2(t;p)$ and $f(x,0)=h(x;p)$ where $f,g_1,g_2,h$ are all $\alpha$-Holder continuous in $(x,t)$. Hence solution exists for...

I cannot believe I am asking this but here we go. This is from literature related to parabolic equations. Let $D$ be a bounded $n+1$ dimensional domain in $R^{n+1}$, $(x,t)=(x_1,\dots,x_n,t)$ is a variable point in $R^{n+1}$. D is bounded by a domain $B$ on $t=0$ and a domain $B$ on $t=0$, a doma...

Elliptic equations already exists. I am slightly skeptical about "index theory": this phrase appears in 5 questions, and they are on different topics. While I do not strongly object to the tag, my expectation is that in a year's time we would find it filled mostly with questions about changing...