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Exact Estimates of Solutions to the Robin Boundary Value Problem for Elliptic Non-divergent Second-order Equations in a Neighborhood of the Boundary Conical Point

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Nonlinear Elliptic and Parabolic Problems

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications ((PNLDE,volume 64))

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References

  1. M. Bochniak, M. Borsuk, Dirichlet problem for linear elliptic equations degenerating at a conical boundary point, Analysis. München, Germany, 23, 3 (2003), pp. 225–248.

    MathSciNet  Google Scholar 

  2. M.V. Borsuk, Best-possible estimates of solutions of the Dirichlet problem for linear elliptic nondivergence equations of second-order in a neighborhood of a conical point on the boundary, Math. USSR Sbornik 74 (1993), 185–201.

    MathSciNet  Google Scholar 

  3. M.V. Borsuk, Estimates of solutions of Dirichlet problem for elliptic nondivergence second-order equations in a neighbourhood of a conical boundary point, Differ. Uravn. 30, 1 (1994), pp. 104–108.

    MATH  MathSciNet  Google Scholar 

  4. M.V. Borsuk, On the solvability of the first boundary value problem for second-order elliptic equations in a domain with a conical point on the boundary, Mat. Fiz. Anal. Geom. 4, 4 (1997), pp. 428–452.

    MATH  MathSciNet  Google Scholar 

  5. R. Courant, D. Hilbert, “Methoden der mathematischen Physik”, Bd. 1, Springer-Verlag, Berlin, 1931.

    Google Scholar 

  6. M. Faierman, Regularity of solutions of an elliptic boundary value problem in a rectangle, Comm. in PDE 12 (1987), 285–305.

    MATH  MathSciNet  Google Scholar 

  7. M.G. Garroni, V.A. Solonnikov and Vivaldi M.A., On the oblique derivative problem in an infinite angle, Topological methods in nonlinear analysis 7 (1996), 299–325.

    MathSciNet  Google Scholar 

  8. D. Gilbarg and N.S. Trudinger, “Elliptic Partial Differential Equations of Second Order”, Springer-Verlag, Berlin/Heidelberg/New York, 1977. Revised Third Printing, 1998.

    Google Scholar 

  9. G.H. Hardy, J.E. Littlewood and G. Pólya, “Inequalities”, University Press, Cambridge, 1952.

    Google Scholar 

  10. V.A. Kondrat’ev, Boundary value problem for elliptic equations in domains with conical or angular points, Trudy Moscov. Mat. Obshch. 16 (1967), 209–292.

    Google Scholar 

  11. V.A. Kozlov, V.G. Maz’ya and Rossman J., “Elliptic boundary value problem in domains with point singularities”, AMS. Mathematical surveys and monographs, 52 (1997).

    Google Scholar 

  12. V.A. Kozlov, V.G. Maz’ya and Rossman J., “Spectral problems associated with corner singularities of solutions to elliptic equations”, AMS. Mathematical surveys and monographs, 85 (2001).

    Google Scholar 

  13. G.M. Lieberman, Local estimates for subsolutions and supersolutions of oblique derivative problems for general second-order elliptic equations, Trans. of AMS. 304 (1987), 343–353.

    MATH  MathSciNet  Google Scholar 

  14. G.M. Lieberman, Oblique derivative problems in Lipschitz domains. Continuous boundary data, Bull. Un. Mat. Ital. B (7) 1 (1987), 1185–1210.

    MATH  MathSciNet  Google Scholar 

  15. G.M. Lieberman, Pointwise estimates for oblique derivative problems in nonsmooth domains, J. Diff. Equat. 173 (2001), no. 1, 178–211.

    Article  MATH  MathSciNet  Google Scholar 

  16. Gary M. Lieberman, The nonlinear oblique derivative problem for quasilinear elliptic equations. Nonlinear Analysis. Theory, Methods and Applications, 8 (1984), p. 49–65.

    Article  MATH  MathSciNet  Google Scholar 

  17. Gary M. Lieberman, Second-order parabolic differential equations, World Scientific, Singapore — New Jersey — London — Hong Kong, 1996, 439 p.

    Google Scholar 

  18. H. Reisman, Second-order elliptic boundary value problem in a domain with edges, Comm. in PDE 6 (1995), 1023–1042.

    MathSciNet  Google Scholar 

  19. S.L. Sobolev, “Some applications of functional analysis in mathematical physics”, Trans. of Math. Monographs, 90 (1991). AMS, Providence, Rhode Island.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics and Informatics, University of Warmia and Mazury in Olsztyn, PL-10-957, Olsztyn-Kortowo, Poland

    M. Borsuk & A. Zawadzka

Authors
  1. M. Borsuk
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  2. A. Zawadzka
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Editor information

Editors and Affiliations

  1. Universitá Pierre et Marie Curie, Paris

    Haim Brezis

  2. Rutgers University, New Brunswick, N.J.

    Haim Brezis

  3. Angewandte Mathematik, Universität Zurich, Winterthurerstr. 190, 8057, Zürich, Switzerland

    Michel Chipot

  4. Institute of Applied Mathematics, University of Hannover, Welfengarten 1, 30167, Hannover, Germany

    Joachim Escher

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© 2005 Birkhäuser Verlag Basel/Switzerland

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Borsuk, M., Zawadzka, A. (2005). Exact Estimates of Solutions to the Robin Boundary Value Problem for Elliptic Non-divergent Second-order Equations in a Neighborhood of the Boundary Conical Point. In: Brezis, H., Chipot, M., Escher, J. (eds) Nonlinear Elliptic and Parabolic Problems. Progress in Nonlinear Differential Equations and Their Applications, vol 64. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7385-7_2

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