scholarly journals Existence of strong solutions to the Dirichlet problem for the Griffith energy

2019 ◽  
Vol 58 (4) ◽  
Author(s):  
Antonin Chambolle ◽  
Vito Crismale
Keyword(s):  
Dirichlet Problem ◽  
Strong Solutions

Wω2,p -Solvability of the Cauchy–Dirichlet Problem for Nondivergence Parabolic Equations with BMO Coefficients

2012 ◽  
Vol 64 (1) ◽  
pp. 217-240 ◽  
Author(s):  
Lin Tang
Keyword(s):  
Dirichlet Problem ◽  
Parabolic Equations ◽  
Strong Solutions ◽  
Weighted Spaces ◽  
Bmo Coefficients

AbstractIn this paper, we establish the regularity of strong solutions to nondivergence parabolic equations with BMO coefficients in nondoubling weighted spaces.

scholarly journals Existence theorems on the Dirichlet problem for the equation Δu + f(x, u)=0

1996 ◽  
Vol 39 (1) ◽  
pp. 31-36
Author(s):  
Gabriele Bonanno
Keyword(s):  
Dirichlet Problem ◽  
Bounded Domain ◽  
Positive Solutions ◽  
Lower Order ◽  
Smooth Boundary ◽  
Existence Theorems ◽  
Suitable Condition ◽  
Strong Solutions ◽  
Order Perturbation

In this note we consider the Dirichlet problem Δu + f(x, u)=0 in Ω, u = 0 on ∂Ω here Ω is a bounded domain in ℝn(n≧3), with smooth boundary ∂Ω. We prove the existence of strong solutions to the previous problem, which are positive if f satisfies a suitable condition. As a consequence we find that the problem with , may have positive solutions even if g is not a lower-order perturbation of Next We examine the case .

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