Geodesic
Local Aleksandrov–Bakelman type maximum estimate for solutions to elliptic equations on a book-type stratified set
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 50, Tome 519 (2022), pp. 105-113 
F. D. Mironenko; A. I. Nazarov. Local Aleksandrov–Bakelman type maximum estimate for solutions to elliptic equations on a book-type stratified set. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 50, Tome 519 (2022), pp. 105-113. http://geodesic.mathdoc.fr/item/ZNSL_2022_519_a4/
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     author = {F. D. Mironenko and A. I. Nazarov},
     title = {Local {Aleksandrov{\textendash}Bakelman} type maximum estimate for solutions to elliptic equations on a book-type stratified set},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {105--113},
     year = {2022},
     volume = {519},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2022_519_a4/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

In the last decades studies of partial differential equations on complex structures have been gaining their popularity. In particular, we notice equations on so-called stratified sets. We prove the Aleksandrov–Bakelman type maximum principle for linear elliptic second order equation on a “book” type stratified set.

[1] D. E. Apushkinskaya, A. I. Nazarov, “Linear two-phase Venttsel problems”, Arkiv för matematik, 39:2 (2001), 201–222 | DOI | MR

[2] D. E. Apushkinskaya, A. I. Nazarov, “Hölder estimates of solutions to initial-boundary value problems for parabolic equations of nondivergent form with Wentzel boundary condition”, Amer. Math. Soc. Transl. Ser. 2, 164 (1995), 1–13 | MR

[3] R. Rokafellar, Vypuklyi analiz, Mir, M., 1973

[4] Y. Luo, “An Aleksandrov-Bakelman type maximum principle and applications”, J. Differ. Equations, 101:2 (1993), 213–231 | DOI | MR

[5] A. D. Aleksandrov, “Nekotorye otsenki, kasayuschiesya zadachi Dirikhle”, DAN SSSR, 134:5 (1960), 1001–1004

[6] D. E. Apushkinskaya, A. I. Nazarov, “Lemma o normalnoi proizvodnoi i vokrug nee”, Usp. matem. nauk, 77 (2022), 3–68

[7] A. I. Nazarov, “Printsip maksimuma A.D. Aleksandrova”, Sovremennaya matematika i ee prilozheniya, 29, 2005, 127–143

[8] I. Ya. Bakelman, “K teorii kvazilineinykh ellipticheskikh uravnenii”, Sib. matem. zh., 2 (1961), 179–186

[9] A. I. Nazarov, N. N. Uraltseva, “Vypuklo-monotonnye obolochki i otsenka maksimuma resheniya parabolicheskogo uravneniya”, Zap. nauchn. semin. POMI, 147, 1985, 95–109

[10] S. N. Oschepkova, O. M. Penkin, “Teorema o srednem dlya ellipticheskogo operatora na stratifitsirovannom mnozhestve”, Matem. zam., 81 (2007), 417–426 | MR