ON SOME PROPERTIES OF GENERALIZED SOLUTIONS OF LINEAR EQUATIONS OF ELLIPTIC AND PARABOLIC TYPE.
Abstract
Considered are weak solutions in W(1,0)sub 2 (Omega x (0,T)) (omega is a space domain) of linear parabolic equation delta u/delta t - Lu = f + div g, where L is the sum of an elliptic second-order operator in divergence form plus lower-order terms. The existence and uniqueness theory of Ladyzhenskaya and Ural'tseva for weak solutions of the first mixed problem involves requiring that the lower-order terms be in certain L sub p classes. It is shown by example that some of these requirements are necessary for uniqueness. Some similar results are also given concerning elliptic problems and concerning the Holder continuity of the solutions. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 08, 1967
- Accession Number
- AD0650398
Entities
People
- A. V. Ivanov
Organizations
- Johns Hopkins University Applied Physics Laboratory