Mollification of $\mathcal{D}$-solutions to Fully Nonlinear PDE Systems

Nikos Katzourakis

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arXiv · 1508.05519

Mollification of $\mathcal{D}$-solutions to Fully Nonlinear PDE Systems

Nikos Katzourakis

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Abstract

In a recent paper (arXiv:1501.06164) the author has introduced a new theory of generalised solutions which applies to fully nonlinear PDE systems of any order and allows the interpretation of merely measurable maps as solutions. This approach is duality-free and builds on the probabilistic representation of limits of difference quotients via Young measures over certain compactifications of the "state space". Herein we establish a systematic regularisation scheme of this notion of solution which, by analogy, is the counterpart of the usual mollification by convolution of weak solutions and of the mollification by sup/inf convolutions of viscosity solutions.

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Nikos Katzourakis. 2015-08-22. Mollification of $\mathcal{D}$-solutions to Fully Nonlinear PDE Systems. https://arxiv.org/abs/1508.05519

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