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Zeitschrift für Analysis und ihre Anwendungen


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Volume 13, Issue 3, 1994, pp. 463–476
DOI: 10.4171/ZAA/501

Published online: 1994-09-30

The Smoothness of Solutions to Nonlinear Weakly Singular Integral Equations

Arvet Pedas[1] and Gennadi Vainikko[2]

(1) Tartu University, Estonia
(2) Tartu University, Estonia

The differential properties of a solution of a nonlinear multidimensional weakly singular integral equation of the Uryson type on an open bounded set $G \in \mathbb R^n$ are examined. Showing that the solution belongs to special weighted space of smooth functions, the growth of the derivatives near the boundary is described.

Keywords: Smoothness of solutions, weakly singular integral equations

Pedas Arvet, Vainikko Gennadi: The Smoothness of Solutions to Nonlinear Weakly Singular Integral Equations. Z. Anal. Anwend. 13 (1994), 463-476. doi: 10.4171/ZAA/501