Lectures on Elliptic Partial Differential Equations
Differential equations, partial Mathematical optimization Partial Differential Equations Calculus of Variations and Optimal Control Optimization
Imprint: Edizioni della Normale
2018
1st ed. 2018.
EISBN 8876426515
Variational aspects of some classes of elliptic problems.
Classical regularity theory for linear problems.
Interior regularity for nonlinear equations.
Regularity for systems.
Viscosity solutions.
Appendices - A. Some basic facts concerning Sobolev spaces.
B. Miscellaneous results in real and harmonic analysis.
C. Hausdorff measures.
D. Some tools from convex and nonsmooth analysis.
The book originates from the Elliptic PDE course given by the first author at the Scuola Normale Superiore in recent years. It covers the most classical aspects of the theory of Elliptic Partial Differential Equations and Calculus of Variations, including also more recent developments on partial regularity for systems and the theory of viscosity solutions.
Classical regularity theory for linear problems.
Interior regularity for nonlinear equations.
Regularity for systems.
Viscosity solutions.
Appendices - A. Some basic facts concerning Sobolev spaces.
B. Miscellaneous results in real and harmonic analysis.
C. Hausdorff measures.
D. Some tools from convex and nonsmooth analysis.
The book originates from the Elliptic PDE course given by the first author at the Scuola Normale Superiore in recent years. It covers the most classical aspects of the theory of Elliptic Partial Differential Equations and Calculus of Variations, including also more recent developments on partial regularity for systems and the theory of viscosity solutions.
