TS Trần Vũ Khanh

Abstract: The d-bar-Neumann problem is one of the most important and natural examples of non-elliptic boundary value problems. It owes its importance to the Cauchy-Riemann problem from which it originates. The main tools to prove regularity of solutions of this problem are various L^2-estimates such as subelliptic, superlogarithmic, compactness estimates,... In this talk, we introduce a general estimate for "gain of regularity" of solutions of this problem and give our recent results about necessary and sufficient conditions for this estimate.

VARIATIONAL INEQUALITY AND ELLIPTIC OPTIMAL CONTROL PROBLEMS

  TS Bùi Trọng Kiên

Abstract: In the report we present some recent results on the solution existence and solution stability of variational inequalities, relations between variational inequality and optimization. We also present results on the solution stability of optimal control problems governed by elliptic equations. The content of the report consists of:

• Variational inequality and its relations with optimization
•  Solution existence of variational inequalities
• Solution stability of variational inequalities
• Solution stability of optimal control problems governed by elliptic partial differential equations