$ L_p$-solubility of the Dirichlet problem for the heat equation in non-cylindrical domains

2002 ◽  
Vol 193 (9) ◽  
pp. 1243-1279 ◽  
Author(s):  
Yu A Alkhutov
Keyword(s):  
Dirichlet Problem ◽  
Heat Equation ◽  
Cylindrical Domains

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.

The Cauchy-Dirichlet problem for the heat equation in Besov spaces

2008 ◽  
Vol 152 (5) ◽  
pp. 638-673
Author(s):  
E. Zadrzyńska ◽  
W. M. Zajaczkowski
Keyword(s):  
Dirichlet Problem ◽  
Heat Equation ◽  
Besov Spaces

scholarly journals Dirichlet problem of heat equation for C2 domains

1989 ◽  
Vol 80 (1) ◽  
pp. 14-31 ◽  
Author(s):  
Robert Kaufman ◽  
Jang-Mei Wu
Keyword(s):  
Dirichlet Problem ◽  
Heat Equation ◽  
C2 Domains

On a solution of the fuzzy Dirichlet problem for the heat equation

2016 ◽  
Vol 103 ◽  
pp. 67-76 ◽  
Author(s):  
N.A. Gasilov ◽  
Ş. Emrah Amrahov ◽  
A.G. Fatullayev
Keyword(s):  
Dirichlet Problem ◽  
Heat Equation
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