Tags » Maximum Principle

Harnack inequality implies Holder continuity

We will show a basic argument why Harnack inequality implies Holder continuity. Assume is a weak solution to a uniform elliptic equation

in . Assume we have Harnack inequality (Indeed we do have due to Moser), i.e. 83 more words

Elliptic Theory

A Key Technique of Environmental Economics

Dynamic optimisation, also known as optimal control, is one of the most important techniques of environmental and natural resource economics.  Although it’s difficult,  the basics should be a compulsory element of graduate-level courses in these fields. 1,862 more words

Environment (general)

Newtonian Potential

— 1. Definition of Newtonian Potential —

Definition 1 Let be a bounded open set, we define the Newtonian potential of is the function on by…

885 more words
Elliptic Theory

Behavior of harmonic functions comparing with a Green's function

Theorem Let , satisfies

If there exists such that

If as , then in .

Proof: Without loss of generality assume on , or we can add a large constant on to make it positive on boundary.

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Elliptic Theory