ON SOME PROPERTIES OF GENERALIZED SOLUTIONS OF LINEAR EQUATIONS OF ELLIPTIC AND PARABOLIC TYPE.
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JOHNS HOPKINS UNIV SILVER SPRING MD APPLIED PHYSICS LAB
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Considered are weak solutions in W1,0sub 2 Omega x 0,T omega is a space domain of linear parabolic equation delta udelta 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 Uraltseva 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
- Numerical Mathematics