All Questions

Let $T_t$ a Feller semigroup (see this) and let $(A,D(A))$ its infinitesimal generator. If A is a bounded operator it is easy to show that the Feller semi-group is $e^{tA}$. Is this formula always ...

Let $\Omega$ be a bounded open domain and $v:\Omega\to\mathbb{R}^n$. Consider the following elliptic operator in divergence form, defined on smooth functions $u: \Omega \to \mathbb{R}$ \begin{align} L ...

In which reference book can I find a proof that the eigenvalue of the Laplace operator in a domain $\Omega \subset \mathbb R^d$ with $d \ge 1$ are given by $$ \lambda_1 = \min_{u \in H^1_0(\Omega), \|...

Let us consider \begin{align*} (-\Delta)^s u &= 0 && x \in B_r(0) \\ u&=0 && x \in \mathbb R^N \setminus B_r(0), \end{align*} where $$ (-\Delta)^s u(x) = \int_{\mathbb{R}^N} \...

Let $\Omega\subseteq\mathbb{R}^N$ be an open, bounded connected set having Lipschitz uniform boundary. Moreover let $d\in L^{\infty}(\Omega,\mathbb{R}^M),\ d_1(x),d_2(x),\dots, d_M(x)>d>0,\ \...

Let $T(t)$ be a $C_0$-semigroup on Banach space $X$, and $A$ its generator. By Lumer-Philipps theorem we know that if $A$ is densely defined and m-dissipative operator then it generates a $C_0$-...