

Steklov Mathematical Institute Seminar
March 20, 2008 16:00, Moscow, Steklov Mathematical Institute of RAS, Conference Hall (8 Gubkina)






Some strengthening of the property of Hölder continuity of solutions of a secondorder elliptic equation
A. K. Gushchin^{} 
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Abstract:
It is well known (De Giorgi, Nash), that generalized solutions of a secondorder elliptic equation with measurable bounded coefficients are Hölder continuous in the interior of the domain. The talk describes the properties which are intermediate between the integral property of a solution to belong to the Sobolev space and the pointwise property of its interior Hölder continuity. All these properties are united by using the special function space. Any solution belongs to the introduced space. This inclusion gives some new properties which do not follow from Hölder continuity and belonging to the Sobolev space. In near terms analogous global properties for solutions of the Dirichlet problem with integrable square boundary function were studied.

