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Uspekhi Mat. Nauk, 1972, Volume 27, Issue 6(168), Pages 67–138 (Mi umn5140)  

This article is cited in 39 scientific papers (total in 39 papers)

Non-linear potential theory

V. G. Maz'ya, V. P. Havin


Full text: PDF file (3459 kB)
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English version:
Russian Mathematical Surveys, 1972, 27:6, 71–148

Bibliographic databases:

UDC: 517.4+517.5
MSC: 31C45, 31A15
Received: 10.01.1972

Citation: V. G. Maz'ya, V. P. Havin, “Non-linear potential theory”, Uspekhi Mat. Nauk, 27:6(168) (1972), 67–138; Russian Math. Surveys, 27:6 (1972), 71–148

Citation in format AMSBIB
\Bibitem{MazHav72}
\by V.~G.~Maz'ya, V.~P.~Havin
\paper Non-linear potential theory
\jour Uspekhi Mat. Nauk
\yr 1972
\vol 27
\issue 6(168)
\pages 67--138
\mathnet{http://mi.mathnet.ru/umn5140}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=409858}
\zmath{https://zbmath.org/?q=an:0247.31010}
\transl
\jour Russian Math. Surveys
\yr 1972
\vol 27
\issue 6
\pages 71--148
\crossref{https://doi.org/10.1070/RM1972v027n06ABEH001393}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. G. Maz'ya, V. P. Havin, “Use of $(p,l)$-capacity in problems of the theory of exceptional sets”, Math. USSR-Sb., 19:4 (1973), 547–580  mathnet  crossref  mathscinet  zmath
    2. V. G. Maz'ya, “On $(p,l)$-capacity, inbedding theorems, and the spectrum of a selfadjoint elliptic operator”, Math. USSR-Izv., 7:2 (1973), 357–387  mathnet  crossref  mathscinet  zmath
    3. Hans Wallin, “Metrical characterization of conformal capacity zero”, Journal of Mathematical Analysis and Applications, 58:2 (1977), 298  crossref
    4. Norman G. Meyers, “Integral inequalities of Poincaré and Wirtinger type”, Arch Rational Mech Anal, 68:2 (1978), 113  crossref  mathscinet  zmath
    5. S. K. Vodop'yanov, V. M. Gol'dstein, Yu. G. Reshetnyak, “On geometric properties of functions with generalized first derivatives”, Russian Math. Surveys, 34:1 (1979), 19–74  mathnet  crossref  mathscinet  zmath
    6. A. N. Kochubei, “Elliptic operators with boundary conditions on a subset of measure zero”, Funct. Anal. Appl., 16:2 (1982), 137–139  mathnet  crossref  mathscinet  zmath  isi
    7. V. G. Maz'ya, T. O. Shaposhnikova, “Theory of multipliers in spaces of differentiable functions”, Russian Math. Surveys, 38:3 (1983), 23–95  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    8. G. Maso, G. Paderni, “Variational inequalities for the biharmonic operator with variable obstacles”, Annali di Matematica, 153:1 (1988), 203  crossref  mathscinet  zmath  isi
    9. S. K. Vodop'yanov, “Potential theory on homogeneous groups”, Math. USSR-Sb., 66:1 (1990), 59–81  mathnet  crossref  mathscinet  zmath  isi
    10. N. N. Tarkhanov, “Approximation on compact sets by solutions of systems with surjective symbol”, Russian Math. Surveys, 48:5 (1993), 103–145  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    11. A. A. Kon'kov, “On the dimension of the solution space of elliptic systems in unbounded domains”, Russian Acad. Sci. Sb. Math., 80:2 (1995), 411–434  mathnet  crossref  mathscinet  zmath  isi
    12. A I Kirillov, “Infinite-dimensional analysis and quantum theory as semimartingale calculus”, Russ Math Surv, 49:3 (1994), 43  mathnet  crossref  mathscinet  zmath  isi
    13. Gianni Dal Maso, Igor V. Skrypnik, “Asymptotic behaviour of nonlinear Dirichlet problems in perforated domains”, Annali di Matematica, 174:1 (1998), 13  crossref  mathscinet  zmath
    14. N. O. Belova, “Ob isklyuchitelnykh mnozhestvakh v $L_p$-teorii potentsiala”, Vladikavk. matem. zhurn., 1:1 (1999), 5–22  mathnet  mathscinet  zmath  elib
    15. A. G. Kusraev, S. S. Kutateladze, “Unsolved nonstandard problems”, Vladikavk. matem. zhurn., 2:2 (2000), 26–45  mathnet  mathscinet  zmath  elib
    16. Pirro Oppezzi, Anna Maria Rossi, “Unilateral problems with measure data”, Nonlinear Analysis: Theory, Methods & Applications, 43:8 (2001), 1057  crossref
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    19. Labutin, DA, “Potential estimates for a class of fully nonlinear elliptic equations”, Duke Mathematical Journal, 111:1 (2002), 1  crossref  mathscinet  zmath  isi
    20. Virginia De Cicco, “Limits of nonlinear weighted Dirichlet problems in varying domains”, Nonlinear Analysis: Theory, Methods & Applications, 48:2 (2002), 247  crossref
    21. Latvala V., “A Strong Lebesgue Point Property for Sobolev Functions”, Proc. Amer. Math. Soc., 132:8 (2004), 2331–2338  crossref  isi
    22. J. E. Brennan, “Thomson's theorem on mean square polynomial approximation”, St. Petersburg Math. J., 17:2 (2006), 217–238  mathnet  crossref  mathscinet  zmath  elib
    23. Niels Jacob, René L. Schilling, “Towards an L p Potential Theory for Sub–Markovian Semigroups: Kernels and Capacities”, Acta Math Sinica, 22:4 (2006), 1227  crossref  mathscinet  zmath  isi
    24. S. K. Vodop'yanov, N. A. Kudryavtseva, “Nonlinear potential theory for Sobolev spaces on Carnot groups”, Siberian Math. J., 50:5 (2009), 803–819  mathnet  crossref  mathscinet  isi  elib
    25. Maly J., Swanson D., Ziemer W.P., “Fine Behavior of Functions Whose Gradients Are in an Orlicz Space”, Studia Math., 190:1 (2009), 33–71  crossref  isi
    26. Vladimir Kondratiev, Vladimir Maz'ya, Mikhail Shubin, “Gauge Optimization and Spectral Properties of Magnetic Schrödinger Operators”, Communications in Partial Differential Equations, 34:10 (2009), 1127  crossref
    27. St. Petersburg Math. J., 22:1 (2011), 41–53  mathnet  crossref  mathscinet  zmath  isi  elib
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    29. Scheven Ch., “Elliptic Obstacle Problems with Measure Data: Potentials and Low Order Regularity”, Publ. Mat., 56:2 (2012), 327–374  crossref  isi
    30. A. Almeida, P. Harjulehto, P. Hästö, T. Lukkari, “Riesz and Wolff potentials and elliptic equations in variable exponent weak Lebesgue spaces”, Annali di Matematica, 2013  crossref
    31. A. L. Volberg, V. Ya. Èiderman, “Non-homogeneous harmonic analysis: 16 years of development”, Russian Math. Surveys, 68:6 (2013), 973–1026  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    32. Paolo Baroni, Tuomo Kuusi, Giuseppe Mingione, “Borderline gradient continuity of minima”, J. Fixed Point Theory Appl, 2014  crossref
    33. Habermann J., “Global Gradient Estimates For Non-Quadratic Vector-Valued Parabolic Quasi-Minimizers”, Nonlinear Anal.-Theory Methods Appl., 114 (2015), 42–73  crossref  isi
    34. A. N. Baykin, S. K. Vodop'yanov, “Capacity estimates, Liouville's theorem, and singularity removal for mappings with bounded $(p,q)$-distortion”, Siberian Math. J., 56:2 (2015), 237–261  mathnet  crossref  mathscinet  isi  elib  elib
    35. N. Tarkhanov, A. A. Shlapunov, “Sturm–Liouville problems in weighted spaces in domains with nonsmooth edges. I”, Siberian Adv. Math., 26:1 (2016), 30–76  mathnet  crossref  crossref  mathscinet  elib
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    38. S. K. Vodopyanov, “Differentiability of mappings of the Sobolev space $W^1_{n-1}$ with conditions on the distortion function”, Siberian Math. J., 59:6 (2018), 983–1005  mathnet  crossref  crossref  isi
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