Ennio de Giorgi Selected Papers Book

Biography     1
Prizes and academic awards     1
Teaching and academic engagements     2
The activities out of Pisa     3
Civil, political, and religious engagement     4
The scientific work of Ennio De Giorgi     5
Complete list of De Giorgi's scientific publications     5
From the juvenile papers to Plateau's Problem and the solution of Hilbert's 19th Problem     19
The first articles     19
The development of the theory of perimeters     20
The solution of Hilbert's 19th Problem     21
The Plateau Problem and the Bernstein Theorem     22
Partial differential equations and the foundations of [Gamma]-convergence     23
The examples of nonuniqueness     23
Gevrey classes and hyperbolic equations     24
Analytic solutions of equations with constant coefficients     25
The foundations of [Gamma]-convergence     26
Asymptotic problems in the Calculus of Variations     27
The developments of [Gamma]-convergence     27
Semicontinuity and relaxation problems     29
Evolution problems for nondifferentiable functionals     30
The most recent developments in the Calculus of Variations     31
Free discontinuity problems     31
Mean curvature evolution     31
Minimizing movements     32
Minimal surfaces in metric spaces     33
The work on Foundations of Mathematics     33
The Seminar on Foundations     33
The Free Construction Principle     35
The Frame Theory and the Ample Theory     36
The basic theories     36
The theories of 2000     37
Remarks on some of the analytic works of Ennio De Giorgi   Louis Nirenberg     38
De Giorgi's contribution to the regularity theory of elliptic equations   Luis Caffarelli     42
Selected papers     49
Definition and analytic expression of the perimeter of a set     50
Definizione ed espressione analitica del perimetro di un insieme     54
On a general (r - 1)-dimensional measure theory in a r-dimensional space     58
Su una teoria generate della misura (r - 1)-dimensionale in uno spazio ad r dimensioni     79
A uniqueness theorem for the Cauchy problem relative to linear partial differential equations of parabolic type     100
An example of non-unique solution to the Cauchy problem, for a partial differential equation of parabolic type     107
New theorems on (r - 1)-dimensional measures in r-dimensional space     111
Nuovi teoremi relativi alle misure (r -1)-dimensionali in uno spazio ad r dimensioni     128
Some applications of a K-dimensional measure theory to the calculus of variations     145
Alcune applicazioni al calcolo delle variazioni di una teoria della misura K-dimensionale     147
On the differentiability and the analyticity of extremals of regular multiple integrals     149
Sulla differenziabilita e l'analiticita delle estremali degli integrali multipli regolari     167
On the isoperimetric property of the hypersphere in the class of sets whose oriented boundary has finite measure     185
Sulla proprieta isoperimetrica dell'ipersfera, nella classe degli insiemi aventi frontiera orientata di misura finita     198
Complements to the (n - 1)-dimensional measure theory in a n-dimensional space     212
Area-minimizing oriented boundaries     231
An extension of Bernstein theorem     264
Hypersurfaces of minimal measure in pluridimensional Euclidean spaces     271
Removable singularities of minimal hypersurfaces     278
An example of discontinuous extremals for a variational problem of elliptic type     285
Un esempio di estremali discontinue per un problema variazionale di tipo ellittico     288
Minimal Cones and the Bernstein Problem      291
An a priori estimate related to nonparametric minimal surfaces     316
A representation formula for analytic functions in R[superscript n]     331
Una formula di rappresentazione per funzioni analitiche in R[superscript n]     335
A direct proof of the existence of analytic solutions in the real plane of partial differential equations with constant coefficients     339
Una dimostrazione diretta dell'esistenza di soluzioni analitiche nel piano reale di equazioni a derivate parziali a coefficienti costanti     350
Convergence of the energy integrals for second order elliptic operators     361
Sulla convergenza degli integrali dell'energia per operatori ellittici del secondo ordine     380
On the convergence of some sequences of area-like integrals     399
Sulla convergenza di alcune successioni d'integrali del tipo dell'area     414
[Gamma]-convergence and G-convergence     429
[Gamma]-convergenza e G-convergenza     437
On hyperbolic equations with coefficients depending on time only     445
Convergence problems for functionals and operators     487
On a type of variational convergence     517
Evolution problems in metric spaces and steepest descent curves     527
Generalized limits in Calculus of Variations     534
A framing theory for the Foundations of Mathematics     570
A self-reference oriented theory for the foundations of mathematics     583
Introduction to free-discontinuity problems     634
Existence theorem for a minimum problem with free discontinuity set     654
New functionals in Calculus of Variations     679
Conjectures on limits of some quasilinear parabolic equations and flow by mean curvature     690
New problems on minimizing movements     699
Lectio Magistralis: "The sapiential value of Mathematics"     714
Lectio Magistralis "Il valore sapienziale della matematica"     720
Fundamental principles of Mathematics     726
Technical complements to the lecture of E. De Giorgi     734
Introducing basic theories for the Foundations of Mathematics     745
Una proposta di teoria base dei Fondamenti della Matematica     758
An introduction of variables into the frame of the basic theories for the Foundations of Mathematics     771
Introduzione delle variabili nel quadro delle teorie base dei Fondamenti della Matematica     783
General Plateau problem and geodesic functionals     795
Conjectures about some evolution problems     801
Congetture riguardanti alcuni problemi di evoluzione     814
Towards the axiomatic systems of the third millennium in Mathematics, Logic, and Computer Science     827
Truth and judgments within a new axiomatic framework     846
Overcoming set-theoretic reductionism in search of wider and deeper mutual understanding between Mathematicians and scholars of different scientific and human disciplines     867
Dal superamento del riduzionismo insiemistico alla ricerca di una piu ampia e profonda comprensione tra matematici e altri studiosi di altre discipline scientifiche ed umanistiche     878