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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



Elliptic equations in convex domains

Author: V. Maz′ya
Original publication: Algebra i Analiz, tom 29 (2017), nomer 1.
Journal: St. Petersburg Math. J. 29 (2018), 155-164
MSC (2010): Primary 35J05; Secondary 35J85
Published electronically: December 27, 2017
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Abstract | References | Similar Articles | Additional Information

Abstract: A short survey of a series of results by the author, partly obtained in collaboration with Yu. Burago.

References [Enhancements On Off] (What's this?)

  • 1. Ya. Alkhutov and V. G. Maz'ya, $ L^{1,p}$-coercitivity and estimates of the Green function of the Neumann problem in a convex domain, Probl. Mat. Anal. 73 (2013), 3-16; English transl., J. Math. Sci. 196 (2014), no. 3, 245-261. MR 3391293
  • 2. Yu. D. Burago, V. G. Maz'ya, and V. D. Sapozhnikova, On the potential of a double layer for non-regular domains, Dokl. Akad. Nauk SSSR 147 (1962), no. 3, 523-525; English transl., Soviet Math. Dokl. 6 (1962), 1640-1642. MR 0145095
  • 3. Yu. D. Burago and V. G. Maz'ya, Certain questions of potential theory and function theory for regions with irregular boundaries, Zap. Nuchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 3 (1967), 1-152; English transl., Sem. Math. V. A. Steklov Math. Inst. Leningrad 3 (1969), 1-68. MR 0240284 (39:1633) and MR 0227447
  • 4. A. Cianchi and V. G. Maz'ya, Global boundedness of the gradient for a class of nonlinear elliptic systems, Arch. Ration. Mech. Anal. 212 (2014), no. 1, 129-177. MR 3162475
  • 5. -, Gradient regularity via rearrangements for $ p$-Laplacian type elliptic boundary value problems, J. Eur. Math. Soc. 16 (2014), no. 3, 571-595. MR 3165732
  • 6. S. Mayboroda and V. G. Maz'ya, Boundedness of the Hessian of a biharmonic function in a convex domain, Comm. Partial Differential Equation 33 (2008), no. 8, 1439-1454. MR 2450165
  • 7. V. G. Maz'ya, Boundary integral equations, Analysis, IV, Encyclopædia Math. Sci., vol. 27, Springer, Berlin, 1991, pp. 127-222. MR 1098507
  • 8. -, Sobolev spaces with applications to elliptic partial differential equations, 2nd ed., Grundlehren Math. Wiss., Bd. 342, Springer, Heidelberg, 2011. MR 2777530

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Additional Information

V. Maz′ya
Affiliation: Department of Mathematics Linköping University Linköping 58183 Sweden

Keywords: Harmonic function, double layer potential, Poisson equation, Sobolev space
Received by editor(s): September 5, 2016
Published electronically: December 27, 2017
Dedicated: To Yury Burago, a friend of my youth, with love and admiration
Article copyright: © Copyright 2017 American Mathematical Society

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