The spectral theory of linear operators, the equations of mathematical physics.
Main publications:
Bobrov A. N. Regulyarizovannye sledy vysshikh poryadkov operatora Laplasa s potentsialom na simmetricheskikh prostranstvakh ranga 1 // Diff. uravneniya, 1997, 33 (6), 800–804.
Bobrov A. N., Podolskii V. E. O skhodimosti sleda stepeni operatora Laplasa–Beltrami s potentsialom na sfere $S^n$ // Funkts. analiz i ego pril., 1997, 31 (4), 69–72.
Bobrov A. N. Sled operatora Laplasa–Beltrami s potentsialom na poverkhnosti Tsollya // Doklady AN, 1999, 368 (2), 154–156.
Bobrov A. N., Podolskii V. E. Skhodimost regulyarizovannykh sledov stepeni operatora Laplasa–Beltrami s potentsialom na sfere $S^n$ // Matem. sbornik, 1999, 190 (10), 3–16.
Bobrov A. N. Spektralnye svoistva nekotorykh dvumernykh kraevykh zadach // Vestn. Mosk. un-ta. Ser. 1. Matematika. Mekhanika. 2001, 1, 3–6.
