scholarly journals Existence and Stability of Solutions of General Semilinear Elliptic Equations with Measure Data

2013 ◽  
Vol 13 (2) ◽  
Author(s):  
Laurent Véron
Keyword(s):  
Elliptic Equations ◽  
Measure Data ◽  
Unified Theory ◽  
Stability Of Solutions ◽  
Semilinear Elliptic ◽  
The Poisson Equation ◽  
Order Elliptic Operator ◽  
Carathéodory Function ◽  
Existence And Stability ◽  
The Stability

AbstractWe study existence and stability for solutions of −Lu + g(x, u) = ω where L is a second order elliptic operator, g a Caratheodory function and ω a measure in Ω. We present a unified theory of the Dirichlet problem and the Poisson equation. We prove the stability of the problem with respect to weak convergence of the data.

scholarly journals Existence of solutions for some degenerate semilinear elliptic equations with measure data

Mathematica ◽  
2021 ◽  
Vol 63 (86) (1) ◽  
pp. 23-31
Author(s):  
Badajena Arun Kumar ◽  
Pradhan Shesadev
Keyword(s):  
Weak Solution ◽  
Elliptic Problem ◽  
Elliptic Equations ◽  
Existence Of Solutions ◽  
Semilinear Elliptic Equations ◽  
Measure Data ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic

We study the existence of a weak solution for a certain degenerate semilinear elliptic problem.

Symmetry breaking for semilinear elliptic equations on sectorial domains in ℝ2

1991 ◽  
Vol 118 (3-4) ◽  
pp. 327-353
Author(s):  
Song-Sun Lin
Keyword(s):  
Symmetry Breaking ◽  
Poisson Equation ◽  
Elliptic Equations ◽  
Semilinear Elliptic Equations ◽  
Complete Picture ◽  
Fredholm Alternative ◽  
Alternative Theory ◽  
Semilinear Elliptic ◽  
The Poisson Equation ◽  
Sectorial Domains

SynopsisWe first study the Poisson equation Δu =fin Ώω,and, where Ωω= {(rcos θ,rsin θ): 0<r<1, θ ∈(0,ω)} is a sector in ℝ2, ω ∈ (0, 2π), Г0= {(cos θ, sin θ): θ ∈ (0, ω)} and Г1= ∂Ωω− Г0,band λ are in ℝ1. We obtain Schauder-type estimates and Fredholm alternative theory for the problem. We then study the symmetry breaking problem for the Gel'fand equation Δu+ λeu= 0 in Ωωand obtain a complete picture about the relationships among three parameters λ,b, and ω in the problem.

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