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Ukrainian Mathematical Journal

, Volume 50, Issue 10, pp 1483–1495 | Cite as

Estimates of generalized solutions of the Dirichlet problem for quasilinear elliptic equations of the second order in a domain with conical boundary point

  • M. V. Borsuk
  • M. I. Plesha
Article

Abstract

We obtain a priori estimates for generalized second derivatives (in the Sobolev weighted norm) of solutions of the Dirichlet problem for the elliptic equation
$$\frac{d}{{dx_i }}a_i (x,u,u_x ) + a(x,u,u_x ) = 0,x \in G,$$
in the neighborhood of a conical boundary point of the domain G. We give an example that demonstrates that the estimates obtained are almost exact.

Keywords

Generalize Solution Elliptic Equation Dirichlet Problem Integral Identity Nonnegative Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    M. V. Borsuk, “Estimates of generalized solutions of the Dirichlet problem for quasilinear elliptic equations of the second order in the domain with conical boundary point,” Differents. Uravn., 31, No. 6, 1001–1007 (1995).MathSciNetGoogle Scholar
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Copyright information

© Kluwer Academic/Plenum Publishers 1999

Authors and Affiliations

  • M. V. Borsuk
    • 1
  • M. I. Plesha
    • 1
  1. 1.Lvov UniversityLvov

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