On the regularity of solutions to the equation $-\Delta u+b\cdot\nabla u=0$
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 43, Tome 410 (2013), pp. 168-186 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

The equation $-\Delta u+b\cdot\nabla u=0$ is considered. The dependence of the local regularity of a solution $u$ on the properties of the coefficient $b$ is investigated.
@article{ZNSL_2013_410_a6,
     author = {N. Filonov},
     title = {On the regularity of solutions to the equation $-\Delta u+b\cdot\nabla u=0$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {168--186},
     year = {2013},
     volume = {410},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2013_410_a6/}
}
TY  - JOUR
AU  - N. Filonov
TI  - On the regularity of solutions to the equation $-\Delta u+b\cdot\nabla u=0$
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2013
SP  - 168
EP  - 186
VL  - 410
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2013_410_a6/
LA  - en
ID  - ZNSL_2013_410_a6
ER  - 
%0 Journal Article
%A N. Filonov
%T On the regularity of solutions to the equation $-\Delta u+b\cdot\nabla u=0$
%J Zapiski Nauchnykh Seminarov POMI
%D 2013
%P 168-186
%V 410
%U http://geodesic.mathdoc.fr/item/ZNSL_2013_410_a6/
%G en
%F ZNSL_2013_410_a6
N. Filonov. On the regularity of solutions to the equation $-\Delta u+b\cdot\nabla u=0$. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 43, Tome 410 (2013), pp. 168-186. http://geodesic.mathdoc.fr/item/ZNSL_2013_410_a6/

[1] R. Coifman, P. L. Lions, Y. Meyer, S. Semmes, “Compensated compactness and Hardy spaces”, J. Math. Pures Appl., 72:3 (1993), 247–286 | MR | Zbl

[2] L. C. Evans, Partial Differential Equations, AMS, Providence, Rhode Island, 1998 | MR | Zbl

[3] D. Gilbarg, N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, 1983 | MR | Zbl

[4] M. A. Krasnosel'skii, Ya. B. Rutickii, Convex functions and Orlicz spaces, P. Noordfoff Ltd., Groningen, 1961 | MR

[5] O. A. Ladyzhenskaya, N. N. Ural'tseva, Linear and Quasilinear Equations of Elliptic Type, Nauka, M., 1973 | MR

[6] V. G. Mazja, I. E. Verbitsky, “Form boundedness of the general second-order differential operator”, Comm. Pure Appl. Math., 59 (2006), 1286–1329 | DOI | MR

[7] A. I. Nazarov, N. N. Ural'tseva, “The Harnack inequality and related properties for solutions to elliptic and parabolic equations with divergence-free lower-order coefficients”, Algebra Analiz, 23:1 (2011), 136–168 | MR

[8] G. Seregin, L. Silvestre, V. Šverák, A. Zlatoš, “On divergence-free drifts”, J. Different. Equat., 252 (2012), 505–540 | DOI | MR | Zbl

[9] L. Silvestre, V. Vicol, A. Zlatoš, “On the loss of continuity for super-critical drift-diffusion equations”, Arch. Rat. Mech. Anal. (to appear) | MR

[10] G. Stampacchia, “Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus”, Ann. Inst. Fourier (Grenoble), 15:1 (1965), 189–258 | DOI | MR | Zbl

[11] E. M. Stein, Harmonic Analysis, Princeton University Press, Princeton, NJ, 1993 | MR | Zbl