By Emmanuele DiBenedetto,Ugo Pietro Gianazza,Vincenzo Vespri

Degenerate and singular parabolic equations were the topic of intensive study for the final 25 years. regardless of very important achievements, the difficulty of the Harnack inequality for non-negative ideas to those equations, either one of p-Laplacian and porous medium type,  whereas raised via a number of authors, has remained  primarily open. lately huge growth has been made in this factor, to the purpose that, aside from the singular sub-critical diversity, either for the p-laplacian and the porous medium equations, the idea within reason complete.

 It appeared for that reason well timed to track a complete review, that may spotlight the most concerns and in addition the issues that also stay open.  The authors provide a entire remedy of the Harnack inequality for non-negative suggestions to p-laplace and porous medium sort equations, either within the degenerate (p>2 or m>1) and within the singular diversity (1<p<2 or 0<m<1), ranging from the idea of resolution and construction all of the worthy technical tools.

The publication is self-contained. construction on an analogous monograph via  the 1st writer, the authors of the current book focus totally at the Harnack estimates and on their functions: certainly a few recognized regularity effects are given a brand new facts, according to the Harnack inequality. it truly is addressed to all execs lively within the box, and likewise to complex graduate scholars, attracted to realizing the most problems with this attention-grabbing examine field.

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