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Mat. Zametki, 2006, Volume 79, Issue 3, Pages 450–469 (Mi mz2714)  

This article is cited in 5 scientific papers (total in 5 papers)

On Morrey's estimate of the Sobolev norms of solutions of elliptic equations

S. V. Shaposhnikov

M. V. Lomonosov Moscow State University

Abstract: We give a complete proof of Morrey's estimate for the $W^{1,p}$-norm of a solution of a second-order elliptic equation on a domain in terms of the $L_1$-norm of this solution. The dependence of the constant in this estimate on the coefficients of the equation is investigated.

DOI: https://doi.org/10.4213/mzm2714

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English version:
Mathematical Notes, 2006, 79:3, 413–430

Bibliographic databases:

UDC: 517.956
Received: 28.04.2005

Citation: S. V. Shaposhnikov, “On Morrey's estimate of the Sobolev norms of solutions of elliptic equations”, Mat. Zametki, 79:3 (2006), 450–469; Math. Notes, 79:3 (2006), 413–430

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. I. Bogachev, M. Röckner, S. V. Shaposhnikov, “Estimates of densities of stationary distributions and transition probabilities of diffusion processes”, Theory Probab. Appl., 52:2 (2008), 209–236  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. S. V. Shaposhnikov, “On Interior Estimates of the Sobolev Norms of Solutions of Elliptic Equations”, Math. Notes, 83:2 (2008), 285–289  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. V. I. Bogachev, N. V. Krylov, M. Röckner, “Elliptic and parabolic equations for measures”, Russian Math. Surveys, 64:6 (2009), 973–1078  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    4. Dashti M., Stuart A.M., “Uncertainty Quantification and Weak Approximation of an Elliptic Inverse Problem”, SIAM J. Numer. Anal., 49:6 (2011), 2524–2542  crossref  mathscinet  zmath  isi  elib  scopus
    5. Baur B., Grothaus M., “Construction and Strong Feller Property of Distorted Elliptic Diffusion With Reflecting Boundary”, Potential Anal., 40:4 (2014), 391–425  crossref  mathscinet  zmath  isi  elib  scopus
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