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

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Ukrainian Mathematical Journal Aims and scope

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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.

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References

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Authors and Affiliations

  1. Lvov University, Lvov

    M. V. Borsuk & M. I. Plesha

Authors
  1. M. V. Borsuk
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  2. M. I. Plesha
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 10, pp. 1299–1309, October, 1998.

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Borsuk, M.V., Plesha, M.I. Estimates of generalized solutions of the Dirichlet problem for quasilinear elliptic equations of the second order in a domain with conical boundary point. Ukr Math J 50, 1483–1495 (1998). https://doi.org/10.1007/BF02513489

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  • DOI: https://doi.org/10.1007/BF02513489

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