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} << /PageLabels << /Nums [0 << /S /r >> 7 << /S /D >> ] >> >>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