  It is shown that the theory of real symmetric second-order elliptic operators
in divergence form on $\Ri^d$ can be formulated in terms of a regular strongly
local Dirichlet form irregardless of the order of degeneracy. The behaviour of
the corresponding evolution semigroup $S_t$ can be described in terms of a
function $(A,B) \mapsto d(A ;B)\in[0,\infty]$ over pairs of measurable subsets
of $\Ri^d$. Then \[ |(\phi_A,S_t\phi_B)|\leq
e^{-d(A;B)^2(4t)^{-1}}\|\phi_A\|_2\|\phi_B\|_2 \] for all $t>0$ and all
$\phi_A\in L_2(A)$, $\phi_B\in L_2(B)$. Moreover $S_tL_2(A)\subseteq L_2(A)$
for all $t>0$ if and only if $d(A ;A^c)=\infty$ where $A^c$ denotes the
complement of $A$.
