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Excerpt from Problems Solved and Unsolved Concerning Linear and Nonlinear Partial Differential Equations Hausdorff measure of dimension 8. Mandelbrot has raised the question of what the Hausdorff dimension of the possible singularities of weak solutions is in space and time. The -first results on this important question were obtained by V. Scheffer the latest word is the following theorem of Caffarelli, Kohn and Nirenberg [5] The one dimensional Hausdorff measure of the set of singularities of a suitable weak solution in x, t-space is zero. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.