Dirichlet problems for systems of elliptic equations with high order of degeneracy

1978 ◽  
Vol 18 (1) ◽  
pp. 122-126
Author(s):  
S. Rutkauskas
Keyword(s):  
Elliptic Equations ◽  
High Order ◽  
Dirichlet Problems ◽  
Systems Of Elliptic Equations

High-Order, Fast-Direct Methods for Separable Elliptic Equations

1984 ◽  
Vol 21 (4) ◽  
pp. 672-694 ◽  
Author(s):  
Linda Kaufman ◽  
Daniel D. Warner
Keyword(s):  
Elliptic Equations ◽  
Direct Methods ◽  
High Order

Perturbation and Solvability of Initial Lp Dirichlet Problems for Parabolic Equations over Non-cylindrical Domains

2014 ◽  
Vol 66 (2) ◽  
pp. 429-452 ◽  
Author(s):  
Jorge Rivera-Noriega
Keyword(s):  
Dirichlet Problem ◽  
Parabolic Equations ◽  
Elliptic Equations ◽  
Carleson Measure ◽  
Divergence Form ◽  
Second Order ◽  
Linear Operators ◽  
Dirichlet Problems ◽  
Small Perturbations ◽  
Cylindrical Domains

AbstractFor parabolic linear operators L of second order in divergence form, we prove that the solvability of initial Lp Dirichlet problems for the whole range 1 < p < ∞ is preserved under appropriate small perturbations of the coefficients of the operators involved. We also prove that if the coefficients of L satisfy a suitable controlled oscillation in the form of Carleson measure conditions, then for certain values of p > 1, the initial Lp Dirichlet problem associated with Lu = 0 over non-cylindrical domains is solvable. The results are adequate adaptations of the corresponding results for elliptic equations.

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