Mollification of D-solutions to Fully Nonlinear PDE Systems [article]

Nikos Katzourakis
2015 arXiv   pre-print
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
more » ... 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.
arXiv:1508.05519v1 fatcat:ulpkltqzzvfo3lmhvdevjdyi3q