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

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Matematicheskie Zametki, 2006, Volume 79, Issue 3, Pages 450–469
DOI: https://doi.org/10.4213/mzm2714 (Mi mzm2714)

This article is cited in 8 scientific papers (total in 8 papers)

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

S. V. Shaposhnikov

M. V. Lomonosov Moscow State University

Full-text PDF (274 kB) Citations (8)

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

Abstract: We give a complete proof of Morrey's estimate for the

W^{1, p}

$W^{1,p}$ -norm of a solution of a second-order elliptic equation on a domain in terms of the

L_{1}

$L_1$ -norm of this solution. The dependence of the constant in this estimate on the coefficients of the equation is investigated.

Received: 28.04.2005

English version:
Mathematical Notes, 2006, Volume 79, Issue 3, Pages 413–430
DOI: https://doi.org/10.1007/s11006-006-0046-2

Bibliographic databases:

UDC: 517.956

Language: Russian

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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Linking options:

https://www.mathnet.ru/eng/mzm2714

https://doi.org/10.4213/mzm2714

https://www.mathnet.ru/eng/mzm/v79/i3/p450

This publication is cited in the following 8 articles:

Haesung Lee, “Analysis of linear elliptic equations with general drifts and L1-zero-order terms”, Journal of Mathematical Analysis and Applications, 2025, 129425
Haesung Lee, “Uniform approximation by harmonic polynomials for solving the Dirichlet problem of Laplace's equation on a disk”, Lith Math J, 2025
Baur B., Grothaus M., “Construction and Strong Feller Property of Distorted Elliptic Diffusion With Reflecting Boundary”, Potential Anal., 40:4 (2014), 391–425
Benedict Baur, Martin Grothaus, Patrik Stilgenbauer, “Construction of ${\mathcal L}^{{p}}$ -strong Feller Processes via Dirichlet Forms and Applications to Elliptic Diffusions”, Potential Anal, 38:4 (2013), 1233
Dashti M., Stuart A.M., “Uncertainty Quantification and Weak Approximation of an Elliptic Inverse Problem”, SIAM J. Numer. Anal., 49:6 (2011), 2524–2542
V. I. Bogachev, N. V. Krylov, M. Röckner, “Elliptic and parabolic equations for measures”, Russian Math. Surveys, 64:6 (2009), 973–1078
S. V. Shaposhnikov, “On Interior Estimates of the Sobolev Norms of Solutions of Elliptic Equations”, Math. Notes, 83:2 (2008), 285–289
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

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

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Abstract page:	625
Full-text PDF :	304
References:	96
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