Discourse Research 14 March 2014 Today I spent all day long thinking about harnack inequality. I was able to rethink about the comparison result, to prove its validity taking into account our own context and to repurpose a new bounded slope condition, which has to be like the function used in the comparison result, but has to be a specific value at a specific point, and so it needs to be reorganized. Also the comparison result had to be understood not as the set Omega being part of an annulus but the annulus being part of Omega, since we need the center of the annulus to be able to be part of the boundary of Omega. So, some things had to be rethought in this new beginning of my new thought on the Harnack inequality. Now I will need to study the proof of lipschitzianity of solutions done by Mariconda and Treu, and which is based on Clarke’s proofs on the lipschitzianity of solutions coming from the bounded slope conditions, in order to find our own proof , and also to take a new look at the harnack inequality and to think again what do we need to do to achieve its proof.
Posted on: Mon, 17 Mar 2014 20:35:51 +0000
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