Unified theory for abstract parabolic boundary problems—a semigroup approach

摘要: This paper presents and abstract semigroup formulation ofparabolic boundary value problems. Smoothness of solutions, represented by a formula, is the primary object discussion. The generality our approach enables us to treat in unified manner theregularity solutions parabolic equations for large variety nonhomogeneous In particular, presented here allows translate known regularity results elliptic theory directly into solutions. On one hand, recaptures over smooth spatial domains. other however, also covers case conical domains, which standard assumption ofC∞-boundaries violated suitable application recent relevant such concluding section, an general control problem with quadratic performance index presented.