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In this paper, we illustrate a counter example for the converse of a certain conjecture proposed by De Giorgi. De Giorgi suggested a series of conjectures, in which a certain integral condition for singularity or degeneracy of an elliptic operator is satisfied, the solutions are continuous. We construct some singular elliptic operators and solutions such that the integral condition does not hold, but the solutions are continuous.
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참고문헌 (12)
참고문헌 신청
E. De Giorgi / 1957 / Sulla differenziabilita e l'analiticita delle estremali degli integrali multipli regolari / Mem. Accad. Sci. Torino, Cl. Sci. Fis. Mat. Nat 3(3):25~43
E. De Giorgi / 1995 / Congetture sulla continuit delle soluzioni di equazioni lineari ellittiche autoaggiunte a coefficienti illimitati / talk given in Lecce, Unpublished
D. Gilbarg / 1983 / Elliptic Partial Differential Equations of Second Order / Springer-Verlag
C. B. Morrey / 1938 / On the solutions of quasi-linear elliptic partial differential equations / Trans. Amer. Math. Soc 43:126~166
C. B. Morrey / 1943 / Multiple integral problems in the calculus of variations and related topics / Univ. California Publ. Math. (N.S.) 1:1~130
E. De Giorgi / 1995 / Congetture sulla continuit delle soluzioni di equazioni lineari ellittiche autoaggiunte a coefficienti illimitati / talk given in Lecce, Unpublished
D. Gilbarg / 1983 / Elliptic Partial Differential Equations of Second Order / Springer-Verlag
C. B. Morrey / 1938 / On the solutions of quasi-linear elliptic partial differential equations / Trans. Amer. Math. Soc 43:126~166
C. B. Morrey / 1943 / Multiple integral problems in the calculus of variations and related topics / Univ. California Publ. Math. (N.S.) 1:1~130
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