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Added DOI of Caffarelli and Cabré's monograph
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Daniele Tampieri
Daniele Tampieri
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The original references are the works of Pucci [2] and [3] which, however, are written in Italian. A perhaps more accessible introduction to these kind of operators is found in the monograph [1], §2.2, pp. 14-17, by Caffarelli and Cabré: in the latter reference, particularly relevant to your questions are lemma 2.12, §2.2 pp. 15-16 and the final part of remark 2, §2.2 p. 16.

References

[1] Luis A. Caffarelli, Xavier Cabré, Fully nonlinear elliptic equations, (English) Colloquium Publications. 43. Providence, RI: American Mathematical Society (AMS). v, 104 p. (1995), DOI: 10.1090/coll/043, MR1351007, Zbl 0834.35002.

[2] Carlo Pucci, "Operatori ellittici estremanti", (in Italian) Annali di Matematica Pura e Applicata (4) 72 (1966), 141--170, DOI: BF02414332, MR0208150, Zbl 0154.12402.

[3] Carlo Pucci, "Operatori massimanti" (in Italian) Monge-Ampère equations and related topics. Proceedings of a Seminar held in Firenze, September - October 1980, Roma: Istituto Nazionale di Alta Matematica ”Francesco Severi”, 169-176 (1982), Zbl 0519.35076.

The original references are the works of Pucci [2] and [3] which, however, are written in Italian. A perhaps more accessible introduction to these kind of operators is found in the monograph [1], §2.2, pp. 14-17, by Caffarelli and Cabré: in the latter reference, particularly relevant to your questions are lemma 2.12, §2.2 pp. 15-16 and the final part of remark 2, §2.2 p. 16.

References

[1] Luis A. Caffarelli, Xavier Cabré, Fully nonlinear elliptic equations, (English) Colloquium Publications. 43. Providence, RI: American Mathematical Society (AMS). v, 104 p. (1995), MR1351007, Zbl 0834.35002.

[2] Carlo Pucci, "Operatori ellittici estremanti", (in Italian) Annali di Matematica Pura e Applicata (4) 72 (1966), 141--170, DOI: BF02414332, MR0208150, Zbl 0154.12402.

[3] Carlo Pucci, "Operatori massimanti" (in Italian) Monge-Ampère equations and related topics. Proceedings of a Seminar held in Firenze, September - October 1980, Roma: Istituto Nazionale di Alta Matematica ”Francesco Severi”, 169-176 (1982), Zbl 0519.35076.

The original references are the works of Pucci [2] and [3] which, however, are written in Italian. A perhaps more accessible introduction to these kind of operators is found in the monograph [1], §2.2, pp. 14-17, by Caffarelli and Cabré: in the latter reference, particularly relevant to your questions are lemma 2.12, §2.2 pp. 15-16 and the final part of remark 2, §2.2 p. 16.

References

[1] Luis A. Caffarelli, Xavier Cabré, Fully nonlinear elliptic equations, (English) Colloquium Publications. 43. Providence, RI: American Mathematical Society (AMS). v, 104 p. (1995), DOI: 10.1090/coll/043, MR1351007, Zbl 0834.35002.

[2] Carlo Pucci, "Operatori ellittici estremanti", (in Italian) Annali di Matematica Pura e Applicata (4) 72 (1966), 141--170, DOI: BF02414332, MR0208150, Zbl 0154.12402.

[3] Carlo Pucci, "Operatori massimanti" (in Italian) Monge-Ampère equations and related topics. Proceedings of a Seminar held in Firenze, September - October 1980, Roma: Istituto Nazionale di Alta Matematica ”Francesco Severi”, 169-176 (1982), Zbl 0519.35076.

Source Link
Daniele Tampieri
Daniele Tampieri
  • 6.4k
  • 7
  • 30
  • 45

The original references are the works of Pucci [2] and [3] which, however, are written in Italian. A perhaps more accessible introduction to these kind of operators is found in the monograph [1], §2.2, pp. 14-17, by Caffarelli and Cabré: in the latter reference, particularly relevant to your questions are lemma 2.12, §2.2 pp. 15-16 and the final part of remark 2, §2.2 p. 16.

References

[1] Luis A. Caffarelli, Xavier Cabré, Fully nonlinear elliptic equations, (English) Colloquium Publications. 43. Providence, RI: American Mathematical Society (AMS). v, 104 p. (1995), MR1351007, Zbl 0834.35002.

[2] Carlo Pucci, "Operatori ellittici estremanti", (in Italian) Annali di Matematica Pura e Applicata (4) 72 (1966), 141--170, DOI: BF02414332, MR0208150, Zbl 0154.12402.

[3] Carlo Pucci, "Operatori massimanti" (in Italian) Monge-Ampère equations and related topics. Proceedings of a Seminar held in Firenze, September - October 1980, Roma: Istituto Nazionale di Alta Matematica ”Francesco Severi”, 169-176 (1982), Zbl 0519.35076.