Selected papers
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| Format: | Buch |
| Sprache: | English Italian |
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Berlin [u.a.]
Springer
2006
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Datensatz im Suchindex
| _version_ | 1819604543165431808 |
|---|---|
| adam_text | Contents
1 Biography
1.1 Prizes and academic awards.......................................
1.2 Teaching and academic engagements................................
1.3 The activities out of Pisa.......................................
1.4 Civil, political, and religious engagement.......................
2 The scientific work of Ennio De Giorgi
2.1 Complete՝ list of lie Giorgi’s scientific publications ..........
2.2 Prom the juvenile ¡tapers to Plateau’s Problem and the solution
of Hilbert s 19lh Problem......................................
2.2.1 The first articles.......................................
2.2.2 The development of the theory of perimeters..............
2.2.3 The solution of flilberl’s If) Problem.................
2.2.4 The Plateau Problem and the Bernstein Theorem ....
2.3 Partial differential equations and the toi nidations of T-eon vergence
2.3.1 The examples of lioiiuniqueucss..........................
2.3.2 Gevrey classes and hyperbolic equations..................
2.3.3 Analytic solutions of equations with constant coefficients
2.3.1 The foundations of T-convcrgcncc ........................
2.4 Asymptotic problems in the Calculus of Variations................
2.4.1 The developments of T-convergence .......................
2.4.2 Somicontinuity and relaxation problems...................
2.4.3 Kvolutioii problems for nondifferentiable functionals . . .
2.o The most recent developments in the Calculus of Variations . . .
2.3.1 Free discontinuity problems..............................
2.3.2 Mean curvature evolution.................................
2.3.3 Minimizing movements.....................................
2.3.1 Minimal surface s in metric spaces.......................
2.G The work n foundations of Mathematics..........................
2.G.1 The Seminar on Foundations................................
2.G.2 The Free Construction Principle...........................
2.G.3 The frame Theory and the Ample Theory.....................
2.G. I The basic theories.......................................
2.G.3 The theories of 2000 .....................................
1
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3
4
5
5
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21
22
23
23
24
25
26
27
27
29
30
31
31
31
32
33
33
33
35
36
36
37
VIII
Contents
2.7 Remarks on some of the analytic works of Ennio Do Ciorgi, by
Lonis Nirenberg..................................................... 38
2.8 Do Giorgi’s contribution to the regularity theory of elliptic
equations, by Luis Caffarelli....................................... 42
3 Selected papers 49
1. Definition and analytic expression of the perimeter of a set .... 50
la. Definizione ed espressione analitica del perimetro di un insieme . . 54
2. On a general (r — 1 )-dimensional measure theory in a / ֊dimensional
space............................................................... 58
2a. Su una teoria, generale della niisura (r - 1 (-dimensionale in uno
spnzio ad r dimensioni.............................................. 79
3. A uniqueness theorem for the Cauchy problem relative to linear
partial differential equations of parabolic type....................100
4. An example of non-unique solution to the Cauchy problem, for a
partial differential equation of parabolic type.....................107
5. New theorems on (r — 1)-dimensionaI measures in /-dimensional
space.............................................................. Ill
5a. Nuovi teoremi relativi alle misure (r— I )-dimensionali in uno spazio
ad /՛ dimensioni................................................... 128
G. Some applications of a if-dimensional measure theory to the
calculus of variations..............................................145
6a. Alciuie applicazioni al calcolo delle varia.zioni di una teoria della.
misura /V-diinonsionale............................................ 147
7. On the differentiability and the analytieitv of extremals of regular
multiple integrals................................................. 149
7a. Sulla differenziabilita e l’analiticita delle estremali degli integrali
multipli regulari.................................................. 167
8. On the isoperimetric property of the hypersphere in the class of
sets whose oriented boundary has finite measure.....................185
8a. Sulla propriety isoperimetrica dclTipersfera, nella classc degli
insiemi aventi frontiera orientata di misura finita.................198
9. Complements to the (n — 1 )-dimensional measure theory in a
//-dimensional space................................................212
10. Area-minimizing oriented boundaries..................................231
11. An extension of Bernstein theorem....................................264
12. Hypersurfaces of minimal measure in pluridimensional Euclidean
spaces..............................................................271
13. Removable singularities of minimal hypersurfaces....................278
14. An example of discontinuous extremals for a variational problem
of elliptic type ...................................................285
14a. Un esempio di estremali discontinue per un problema variazionalc
di tipo ellittico...................................................288
15. Minimal Cones and the Bernstein Problem.............................291
16. An a priori estimate related to nonparametric minimal surfaces . . 316
17. A representation formula for analytic functions in Rn...............331
Conteutv IX
17a. Una formula di rappresentazioue per funzioni analitiche in R . . 335
18. A direct proof of the oxistouce of analytic .solutions in the real
plane of partial differential equations with constant coefficients . 339
18a. Una dimostrazionc diretta dell esistenza di soluzioni analitiche nel
piano reale di equazioni a derivate parziali a coefficient! cost anti 350
19. Convergence of the energy integrals for second order elliptic
operators .........................................................361
19a. Sulla convergenza degli intcgrali dell’cnorgia per operator! ellittici
del sccoudo ordine.................................................380
20. On the convergence of some sequences of area-like integrals .... 399
20a. Sulla convergenza di alcnnc successioni d’integrali del tipo
dell’area..........................................................414
21. F-convcrgeuce and (7-convorgence ..................................429
21a. r-convergenza e (r-eonvergonza.....................................437
22. On hyperbolic equations with coefficients depending on time only 445
23. Convergence problems for functionals and operators.................487
24. On a type of varial ional convergent·*.............................517
25. Evolution problems in metric spaces and steepest, descent curves . 527
26. Generalized limits in Calculus of Variations.......................534
27. A framing theory for the Foundations of Mathematics................570
28. A self-reference orient ed theory for the foundations of mathematics 583
29. Introduction to free-disconiinuity problems........................634
30. Existence theorem for a minimum problem with free discontinuity
set................................................................654
31. Xew functionals in Calculus of Variations..........................679
32. Conjectures on limits of some quasi linear parabolic equations and
flow lay mean curvature ...........................................690
33. Xew problems on minimizing movements...............................699
34. Lectio Magistralis: The sapiential value of Mathematics”..........714
34a. Lectio Magistralis II valore sapienziale della lnatcmatica’’ .... 720
35. Fundamental principles of Mai hematics.............................726
36. Technical complements to the lecture of E. Do Giorgi...............734
37. Introducing basic theories for the Foundations of Mathematics . . 745
37a. Una propost a di teorin base dci Fondainenti della Matematica . . 758
38. An introduction of variables into the frame of the basic theories for
the Foundations of Mathematics.....................................771
38a. Iutroduxione delle variabili nel quadro delle teoric base dei
Fondainenti della Matematica.......................................783
3 J. General Plateau problem and geodesic functionals...................795
4(). Conjectures about some evolution problems..........................801
40a. Cougetturc riguardanti alcuni problemi di evoluzione...............814
41. Towards the axiomatic systems of the third millennium
in Mathematics. Logic, and Computer Science........................827
12. Truth and judgments within a new axiomatic framework ............816
X
Confluita
-13. Overcoming ael theorelic reductioiiism in search of wider and
dooper mutuai understanding between Matliematicians and
scliolars of different sdentific and human disciplincs .........867
43a. Dal superamento del riduzionismo insiemistico alla ricerca di una
più ampia e profonda comprensione tra matematici e altri studiosi
di altre discipline scientifiche ed umanistiche......................878
|
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| author | De Giorgi, Ennio 1928-1996 |
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| dewey-ones | 510 - Mathematics |
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| discipline | Mathematik |
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| indexdate | 2024-12-23T19:33:22Z |
| institution | BVB |
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| language | English Italian |
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| spellingShingle | De Giorgi, Ennio 1928-1996 Selected papers De Giorgi, Ennio De Giorgi, Ennio 1928-1996 (DE-588)131666762 gnd Mathematik Mathematics Analysis (DE-588)4001865-9 gnd |
| subject_GND | (DE-588)131666762 (DE-588)4001865-9 (DE-588)4143413-4 (DE-588)4006432-3 |
| title | Selected papers |
| title_auth | Selected papers |
| title_exact_search | Selected papers |
| title_full | Selected papers Ennio de Giorgi |
| title_fullStr | Selected papers Ennio de Giorgi |
| title_full_unstemmed | Selected papers Ennio de Giorgi |
| title_short | Selected papers |
| title_sort | selected papers |
| topic | De Giorgi, Ennio De Giorgi, Ennio 1928-1996 (DE-588)131666762 gnd Mathematik Mathematics Analysis (DE-588)4001865-9 gnd |
| topic_facet | De Giorgi, Ennio De Giorgi, Ennio 1928-1996 Mathematik Mathematics Analysis Aufsatzsammlung Bibliografie |
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