Optimal regularity in the optimal switching problem

• In this article we study the optimal regularity for solutions to the following weakly coupled system with interconnected obstacles{min⁡(−Δu1+f1,u1−u2+ψ1)=0min⁡(−Δu2+f2,u2−u1+ψ2)=0 arising in the optimal switching problem with two modes. We derive the optimal C1,1-regularity for the minimal solution under the assumption that the zero loop set L:={ψ1+ψ2=0} is the closure of its interior. This result is optimal and we provide a counterexample showing that the C1,1-regularity does not hold without the assumption L=L0‾. 

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Publikations- och innehållstyp

ref (ämneskategori)

art (ämneskategori)