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Algebra i Analiz, 2011, Volume 23, Issue 1, Pages 136–168 (Mi aa1227)  

This article is cited in 27 scientific papers (total in 27 papers)

Research Papers

The Harnack inequality and related properties for solutions to elliptic and parabolic equations with divergence-free lower-order coefficients

A. I. Nazarov, N. N. Uraltseva

St. Petersburg State University, Department of Mathematics and Mechanics, St. Petersburg, Russia

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English version:
St. Petersburg Mathematical Journal, 2012, 23:1, 93–115

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Received: 12.10.2010

Citation: A. I. Nazarov, N. N. Uraltseva, “The Harnack inequality and related properties for solutions to elliptic and parabolic equations with divergence-free lower-order coefficients”, Algebra i Analiz, 23:1 (2011), 136–168; St. Petersburg Math. J., 23:1 (2012), 93–115

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    1. Silvestre L., Vicol V., “Hölder continuity for a drift-diffusion equation with pressure”, Ann. Inst. H. Poincaré Anal. Non Linéaire, 29:4 (2012), 637–652  crossref  mathscinet  zmath  adsnasa  isi  scopus
    2. J. Math. Sci. (N. Y.), 195:1 (2013), 98–108  mathnet  crossref  mathscinet
    3. St. Petersburg Math. J., 25:2 (2014), 195–203  mathnet  crossref  mathscinet  zmath  isi  elib
    4. Ignatova M., “On the Continuity of Solutions To Advection-Diffusion Equations With Slightly Super-Critical Divergence-Free Drifts”, Adv. Nonlinear Anal., 3:2 (2014), 81–86  crossref  mathscinet  zmath  isi  scopus
    5. Bogachev V.I., Kirillov A.I., Shaposhnikov S.V., “A Stationary Fokker-Planck-Kolmogorov Equation With a Potential”, Dokl. Math., 89:1 (2014), 24–29  crossref  mathscinet  zmath  isi  elib  scopus
    6. Ignatova M., Kukavica I., Ryzhik L., “The Harnack Inequality For Second-Order Elliptic Equations With Divergence-Free Drifts”, Commun. Math. Sci., 12:4 (2014), 681–694  crossref  mathscinet  zmath  isi  scopus
    7. M. D. Surnachev, “O edinstvennosti reshenii zadachi o statsionarnoi diffuzii v neszhimaemom turbulentnom potoke”, Preprinty IPM im. M. V. Keldysha, 2015, 096, 32 pp.  mathnet
    8. Nazarov A.I., Paletskikh A.A., “on the Holder Continuity of Solutions of the Venttsel' Elliptic Problem”, Dokl. Math., 92:3 (2015), 747–751  crossref  mathscinet  zmath  isi  elib  scopus
    9. Hara T., “a Refined Subsolution Estimate of Weak Subsolutions To Second Order Linear Elliptic Equations With a Singular Vector Field”, Tokyo J. Math., 38:1 (2015), 75–98  crossref  mathscinet  zmath  isi  scopus
    10. Kim H., Kim Y.-H., “on Weak Solutions of Elliptic Equations With Singular Drifts”, SIAM J. Math. Anal., 47:2 (2015), 1271–1290  crossref  mathscinet  zmath  isi  scopus
    11. Hara T., “Weak-Type Estimates and Potential Estimates For Elliptic Equations With Drift Terms”, Potential Anal., 44:1 (2016), 189–214  crossref  mathscinet  zmath  isi  elib  scopus
    12. Wang Ya., Wu G., Zhou D., “Refined regularity class of suitable weak solutions to the 3D magnetohydrodynamics equations with an application”, Z. Angew. Math. Phys., 67:6 (2016), 136  crossref  mathscinet  isi  elib  scopus
    13. Frigeri S., Gal C.G., Grasselli M., “On Nonlocal Cahn–Hilliard–Navier–Stokes Systems in Two Dimensions”, J. Nonlinear Sci., 26:4 (2016), 847–893  crossref  mathscinet  zmath  isi  elib  scopus
    14. Jiu Q., Wang Ya., Wu G., “Partial Regularity of the Suitable Weak Solutions to the Multi-dimensional Incompressible Boussinesq Equations”, J. Dyn. Differ. Equ., 28:2 (2016), 567–591  crossref  mathscinet  zmath  isi  scopus
    15. Ignatova M., Kukavica I., Ryzhik L., “The Harnack inequality for second-order parabolic equations with divergence-free drifts of low regularity”, Commun. Partial Differ. Equ., 41:2 (2016), 208–226  crossref  mathscinet  zmath  isi  scopus
    16. Chen G., “Non-divergence parabolic equations of second order with critical drift in Lebesgue spaces”, J. Differ. Equ., 262:3, 2 (2017), 2414–2448  crossref  mathscinet  zmath  isi  scopus
    17. Chen G., Safonov M., “on Second Order Elliptic and Parabolic Equations of Mixed Type”, J. Funct. Anal., 272:8 (2017), 3216–3237  crossref  mathscinet  zmath  isi
    18. J. Burczak, G. Seregin, “$LlogL$-integrability of the velocity gradient for Stokes system with drifts in $L_\infty (BMO^{-1})$”, Kraevye zadachi matematicheskoi fiziki i smezhnye voprosy teorii funktsii. 46, Zap. nauchn. sem. POMI, 459, POMI, SPb., 2017, 37–57  mathnet
    19. T. Shilkin, “On the local smoothness of some class of axi-symmetric solutions to the MHD equations”, Kraevye zadachi matematicheskoi fiziki i smezhnye voprosy teorii funktsii. 46, Zap. nauchn. sem. POMI, 459, POMI, SPb., 2017, 127–148  mathnet
    20. Zhao W., “Persistence of Besov Regularity For a Generalized Drift-Diffusion Equation With Pressure”, Acta Appl. Math., 154:1 (2018), 83–93  crossref  mathscinet  zmath  isi  scopus
    21. Surnachev M.D., “On the Uniqueness of Solutions to Stationary Convection-Diffusion Equations With Generalized Divergence-Free Drift”, Complex Var. Elliptic Equ., 63:7-8, SI (2018), 1168–1184  crossref  mathscinet  zmath  isi  scopus
    22. G. Seregin, “Remarks on Liouville type theorems for steady-state Navier–Stokes equations”, Algebra i analiz, 30:2 (2018), 238–248  mathnet  elib
    23. G. A. Seregin, T. N. Shilkin, “Liouville-type theorems for the Navier–Stokes equations”, Russian Math. Surveys, 73:4 (2018), 661–724  mathnet  crossref  crossref  adsnasa  isi  elib
    24. Miao Q., Xue L., “On the Holder Regularity of the Weak Solution to a Drift-Diffusion System With Pressure”, Calc. Var. Partial Differ. Equ., 57:6 (2018), 153  crossref  mathscinet  zmath  isi  scopus
    25. Apushkinskaya D., “Free Boundary Problems Regularity Properties Near the Fixed Boundary Preface”: Apushkinskaya, D, Free Boundary Problems: Regularity Properties Near the Fixed Boundary, Lect. Notes Math., Lecture Notes in Mathematics, 2218, Springer International Publishing Ag, 2018, V+  mathscinet  isi
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    27. Bobkov V., Takac P., “On Maximum and Comparison Principles For Parabolic Problems With the P-Laplacian”, Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat., 113:2 (2019), 1141–1158  crossref  isi
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