Lecture Notes
Inserted: 22 jul 2002
Year: 2002
Abstract:
In this notes we describe the basic ideas and techniques used to prove existence and uniqueness results for viscosity solution of elliptic partial differential equations. The aim is to give a simple description of the basic ideas and motivations behind the definition of viscosity solution, thus the description is sometimes lacking in details and precision. The first part is devoted to the introduction of the definition of viscosity solution. In the second one we discuss the first order case, giving an example of application and a detailed description of the technique used to prove comparison results. The third, and last, part is devoted to the discussion of general stability results, the Perron's method to prove existence and some remarks on the proof of the comparison result for the second order case.
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