Lectures on elliptic partial differential equations

Introduction Lecture 1 Spaces H(A; ) General notations Spaces H(A;) The space H0(A; ). Extension of functions in Ho(A; ) to Rn. Lecture 2 Regularization Problem of local type. Some generalizations. Lecture 3 Spaces Hm. Extension of functions in Ho(A; ) to Rn. Lecture 4 The mapping . Lecture 5 General Elliptic Boundary Value Problems General theory. Lecture 6 Examples: + , >0, = i=1n {Catalog} >>2 uxi2. Lecture 7 Green's kernel. Relations with unbounded operators. Lecture 8 Complements on Hm() Estimates on Hmo(). Regularity of the function in Hm(). Reproducing kernels. Lecture 9 Complete Continuity. Applications Lecture 10 Operators of order 2 V = H1o (), gij constant. Lecture 11 Formal interpretation: Complementary results. Lecture 12 Operators of order 2m Applications to the Dirichlet's problem. Lecture 13 Applications Regularity in the Interior Statements of theorems Lecture 14 Some remarks. Lecture 15 Regularity at the boundary. Lecture 16 Lecture 17 Completion of the proof of theorem 9.1. Other results. An application of theorem 9.1. Lecture 18 Regularity at the boundary in the case of... Regularity at the boundary for some more problems. Visik-Soboleff Problems Lecture 19 Lecture 20 Application. Aronszajn and Smith Problems[1] Complements on Hm () Lecture 21 Aronszajn-Smith Problems Lecture 22 Lecture 23 Regularity of Green's Kernels Lecture 24 Study at the boundary. Regularity at the Boundary Problems for... Lecture 25 Systems