Construction of elliptic diffusions with reflecting boundary condition and an application to continuous N-particle systems with singular interactions

Abstract. We give a Dirichlet form approach for the construction and analysis of ellip-tic diffusions in Ω ⊂ Rn with reflecting boundary condition. The problem is formulated in an L2-setting w.r.t. a reference measure µ on Ω having an integrable, dx-a.e. positive, density % w.r.t. the Lebesgue measure. The symmetric Dirichlet forms (E%,a, D(E%,a)) we consider are the closure of the symmetric bilinear forms E%,a(f, g) = nX i,j=1 Z Ω ∂if aij ∂jg dµ, f, g ∈ D