Semigroup's Approach to the Study of the Hölder Continuous Regularity for Laplace Equation in Nonsmooth Domain

We will investigate the Dirichlet problem for Laplace equation set in an singular domain with cuspidal point. We look to describe the behavior of the unique solution near the cuspidal point in the framework of the little Hölder space h2σ (Ω) with σ ∈ ]0,1/2[.