The Dirichlet Problem for Second-Order Quasi-Linear Nonuniformly Elliptic Equations

1972 ◽  
pp. 43-52 ◽  
Author(s):  
A. V. Ivanov
Keyword(s):  
Dirichlet Problem ◽  
Elliptic Equations ◽  
Second Order

scholarly journals The Dirichlet Problem for elliptic equations in unbounded domains of the plane

2008 ◽  
Vol 6 (1) ◽  
pp. 47-58 ◽  
Author(s):  
Paola Cavaliere ◽  
Maria Transirico
Keyword(s):  
Dirichlet Problem ◽  
Existence Theorem ◽  
Elliptic Equations ◽  
Unbounded Domains ◽  
Suitable Condition ◽  
Second Order ◽  
Order Linear ◽  
Uniqueness And Existence

In this paper we prove a uniqueness and existence theorem for the Dirichlet problem inW2,pfor second order linear elliptic equations in unbounded domains of the plane. Here the leading coefficients are locally of classVMOand satisfy a suitable condition at infinity.

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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