Author | Oleฤญnik, O. A. author |
---|---|
Title | Second Order Equations With Nonnegative Characteristic Form [electronic resource] / by O. A. Oleฤญnik, E. V. Radkeviฤ |
Imprint | Boston, MA : Springer US, 1973 |
Connect to | http://dx.doi.org/10.1007/978-1-4684-8965-1 |
Descript | VII, 259 p. online resource |
I. The First Boundary Value Problem -- 1. Notation. Auxiliary results. Formulation of the first boundary value problem -- 2. A priori estimates in the spaces Lp (?) -- 3. Existence of a solution of the first boundary value problem in the spaces Lp (?) -- 4. Existence of a weak solution of the first boundary value problem in Hilbert space -- 5. Solution of the first boundary value problem by the method of elliptic regularization -- 6. Uniqueness theorems for weak solutions of the first boundary value problem -- 7. A lemma on nonnegative quadratic forms -- 8. On smoothness of weak solutions of the first boundary value problem. Conditions for existence of solutions with bounded derivatives -- 9. On conditions for the existence of a solution of the first boundary value problem in the spaces of S. L. Sobolev -- II. On the Local Smoothness of Weak Solutions and Hypoellipticity of Second Order Differential Equations -- 1. The spaces Hs -- 2. Some properties of pseudodifferential operators -- 3. A necessary condition for hypoellipticity -- 4. Sufficient conditions for local smoothness of weak solutions and hypoellipticity of differential operators -- 5. A priori estimates and hypoellipticity theorems for the operators of Hรถrmander -- 6. A priori estimates and hypoellipticity theorems for general second order differential equations -- 7. On the solution of the first boundary value problem in nonsmooth domains. The method of M. V. Keldyลก -- 8. On hypoellipticity of second order differential operators with analytic coefficients -- III. Additional Topics -- 1. Qualitative properties of solutions of second order equations with non- negative characteristic form -- 2. The Cauchy problem for degenerating second order hyperbolic equations -- 3. Necessary conditions for correctness of the Cauchy problem for second order equations