ON THE DIRICHLET PROBLEM FOR AN ELLIPTIC OPERATOR IN A CYLINDRICAL DOMAIN OF HILBERT SPACE

1973 ◽  
Vol 21 (3) ◽  
pp. 423-438 ◽  
Author(s):  
N N Frolov
Keyword(s):  
Hilbert Space ◽  
Dirichlet Problem ◽  
Elliptic Operator ◽  
Cylindrical Domain

An abstract Dirichlet problem in the Hilbert space

1997 ◽  
Vol 4 (1) ◽  
pp. 109-116
Author(s):  
Hamza A. S. Abujabal ◽  
Mahmoud M. El-Borai
Keyword(s):  
Hilbert Space ◽  
Dirichlet Problem

scholarly journals Weak Uniqueness for Elliptic Operators in ℝ3 with Time-Independent Coefficients

2006 ◽  
Vol 74 (1) ◽  
pp. 91-100
Author(s):  
Cristina Giannotti
Keyword(s):  
Dirichlet Problem ◽  
Elliptic Operator ◽  
Elliptic Operators ◽  
Second Order ◽  
Weak Uniqueness

The author gives a proof with analytic means of weak uniqueness for the Dirichlet problem associated to a second order uniformly elliptic operator in ℝ3 with coefficients independent of the coordinate x3 and continuous in ℝ2 {0}.

scholarly journals On Dirichlet's boundary value problem for some formally hypoelliptic differntial operators

1988 ◽  
Vol 44 (3) ◽  
pp. 324-349 ◽  
Author(s):  
Niels Jacob
Keyword(s):  
Hilbert Space ◽  
Dirichlet Problem ◽  
Differential Operator ◽  
Boundary Value Problem ◽  
Differential Operators ◽  
Boundary Value ◽  
Divergence Form ◽  
Alternative Theorem ◽  
Sesquilinear Form ◽  
Homogeneous Dirichlet Problem

AbstractFor a class of formally hypoelliptic differential operators in divergence form we prove a generalized Gårding inequality. Using this inequality and further properties of the sesquilinear form generated by the differential operator a generalized homogeneous Dirichlet problem is treated in a suitable Hilbert space. In particular Fredholm's alternative theorem is proved to be valid.

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