I am currently studying Poisson and Laplace equations. This is just a small question that has been causing me some confusion, and I would like some clarification before I resume my study. For example, when we write $\triangle u =0$ in the sense of distributions and u is also a distribution, are we assuming that $u$ is locally integrable. By this, I mean, are we assuming that $u$ is a function that is in $L^1_{loc}$? Thanks very much.
weak solutions need to have local integrability condition?
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analysis
pde