Hausdorff Continuous Solutions of Nonlinear PDEs through the Order Completion Method
نویسنده
چکیده
It was shown in [13] that very large classes of nonlinear PDEs have solutions which can be assimilated with usual measurable functions on the Euclidean domains of definition of the respective equations. In this paper the regularity of these solutions has significantly been improved by showing that they can in fact be assimilated with Hausdorff continuous functions. The method of solution of PDEs is based on the Dedekind order completion of spaces of smooth functions which are defined on the domains of the given equations.
منابع مشابه
Arbitrary Continuous Nonlinear PDEs through the Order Completion Method
In 1994 we showed that very large classes of systems of nonlinear PDEs have solutions which can be assimilated with usual measurable functions on the Euclidean domains of definition of the respective equations. Recently, the regularity of such solutions has significantly been improved by showing that they can in fact be assimilated with Hausdorff continuous functions. The method of solution of ...
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