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Existence and regularity results for some shape optimization problems [[electronic resource] /] / by Bozhidar Velichkov
| Existence and regularity results for some shape optimization problems [[electronic resource] /] / by Bozhidar Velichkov |
| Autore | Velichkov Bozhidar |
| Edizione | [1st ed. 2015.] |
| Pubbl/distr/stampa | Pisa : , : Scuola Normale Superiore : , : Imprint : Edizioni della Normale, , 2015 |
| Descrizione fisica | 1 online resource (362 p.) |
| Disciplina |
510
515.64 |
| Collana | Theses (Scuola Normale Superiore) |
| Soggetto topico |
Calculus of variations
Calculus of Variations and Optimal Control; Optimization |
| ISBN | 88-7642-527-6 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Title Page; Copyright Page; Table of Contents; Preface; Résumé of the main results; Chapter 1 Introduction and Examples; 1.1. Shape optimization problems; 1.2. Why quasi-open sets?; 1.3. Compactness and monotonicity assumptions in the shape optimization; 1.4. Lipschitz regularity of the state functions; Chapter 2 Shape optimization problems in a box; 2.1. Sobolev spaces on metric measure spaces; 2.2. The strong-γ and weak-γ convergence of energy domains; 2.2.1. The weak-γ -convergence of energy sets; 2.2.2. The strong-γ -convergence of energy sets
2.2.3. From the weak-γ to the strong-γ -convergence2.2.4. Functionals on the class of energy sets; 2.3. Capacity, quasi-open sets and quasi-continuous functions; 2.3.1. Quasi-open sets and energy sets from a shape optimization point of view; 2.4. Existence of optimal sets in a box; 2.4.1. The Buttazzo-Dal Maso Theorem; 2.4.2. Optimal partition problems; 2.4.3. Spectral drop in an isolated box; 2.4.4. Optimal periodic sets in the Euclidean space; 2.4.5. Shape optimization problems on compact manifolds; 2.4.6. Shape optimization problems in Gaussian spaces 2.4.7. Shape optimization in Carnot-Caratheodory space2.4.8. Shape optimization in measure metric spaces; Chapter 3 Capacitary measures; 3.1. Sobolev spaces in Rd; 3.1.1. Concentration-compactness principle; 3.1.2. Capacity, quasi-open sets and quasi-continuous functions; 3.2. Capacitary measures and the spaces H1μ; 3.3. Torsional rigidity and torsion function; 3.4. PDEs involving capacitary measures; 3.4.1. Almost subharmonic functions; 3.4.2. Pointwise definition, semi-continuity and vanishing at infinity for solutions of elliptic PDEs Chapter 4 Subsolutions of shape functionals4.1. Introduction; 4.2. Shape subsolutions for the Dirichlet Energy; 4.3. Interaction between energy subsolutions; 4.3.1. Monotonicity theorems; 4.3.2. The monotonicity factors; 4.3.3. The two-phase monotonicity formula; 4.3.4. Multiphase monotonicity formula; 4.3.5. The common boundary of two subsolutions. Application of the two-phase monotonicity formula.; 4.3.6. Absence of triple points for energy subsolutions. Application of the multiphase monotonicity formula; 4.4. Subsolutions for spectral functionals with measure penalization 4.5. Subsolutions for functionals depending on potentials and weights |
| Record Nr. | UNINA-9910299776403321 |
Velichkov Bozhidar
|
||
| Pisa : , : Scuola Normale Superiore : , : Imprint : Edizioni della Normale, , 2015 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Regularity of the One-phase Free Boundaries [[electronic resource] /] / by Bozhidar Velichkov
| Regularity of the One-phase Free Boundaries [[electronic resource] /] / by Bozhidar Velichkov |
| Autore | Velichkov Bozhidar |
| Edizione | [1st ed. 2023.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2023 |
| Descrizione fisica | 1 online resource (249 pages) |
| Disciplina |
519.6
515.64 |
| Collana | Lecture Notes of the Unione Matematica Italiana |
| Soggetto topico |
Mathematical optimization
Calculus of variations Differential equations Calculus of Variations and Optimization Differential Equations Problemes de contorn Funcions analítiques Equacions en derivades parcials |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-031-13238-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910669809303321 |
|
Velichkov Bozhidar
|
||
| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2023 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||