The Hahn-Banach Theorems. Introduction to the Theory of Conjugate Convex Functions. Unbounded Operators. Characterization of Surjective Operators. Weak Topologies. Reflexive Spaces.
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Tikhonov regularization of optimal control problems governed by semi-linear partial differential equations. Time-inconsistent stochastic optimal control problems: A backward stochastic partial differential equations approach. On the system of partial differential equations arising in mean field type control. A variational problem and optimal control.
Towards a geometric variational discretization of compressible fluids: The rotating shallow water equations. Journal of Computational Dynamics, , 6 1 : Analysis and discretization of an optimal control problem for the forced Fisher equation. Optimal control problems for some ordinary differential equations with behavior of blowup or quenching. Preservation of homoclinic orbits under discretization of delay differential equations. Kipka , Yuri S. Optimal control of differential inclusions on manifolds.
Convergence analysis of Euler discretization of control-state constrained optimal control problems with controls of bounded variation. Variational discretization for rotating stratified fluids. Partial differential equations with non-Euclidean geometries.
Spectral theory and nonlinear partial differential equations: A survey. Petropoulou , Panayiotis D. Polynomial solutions of linear partial differential equations.
Taylor expansions of solutions of stochastic partial differential equations. Dichotomy and periodic solutions to partial functional differential equations. Exact solutions of nonlinear partial differential equations.
Regularity results for a time-optimal control problem in the space of probability measures.
Functional Analysis, Sobolev Spaces and Partial Differential Equations
Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Moreover, the wealth of exercises and additional material presented, leads the reader to the frontier of research. The English version is a welcome addition to this list. The first part of the text deals with abstract results in FA and operator theory.