On a singular Liouville-type equation and the Alexandrov isoperimetric inequlity
نویسندگان
چکیده
منابع مشابه
the investigation of the relationship between type a and type b personalities and quality of translation
چکیده ندارد.
Blowup Solutions for a Liouville Equation with Singular Data
We consider the asymptotic analysis and some existence result on blowing up solutions for a semilinear elliptic equation in dimension 2 with nonlinear exponential term, singular sources and Dirichlet boundary condition.
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We consider the boundary value problem ∆u+ε k(x) e = 0 in a bounded, smooth domain Ω in R with homogeneous Dirichlet boundary conditions. Here ε > 0, k(x) is a non-negative, not identically zero function. We find conditions under which there exists a solution uε which blows up at exactly m points as ε→ 0 and satisfies ε ∫ Ω keε → 8mπ. In particular, we find that if k ∈ C(Ω̄), infΩ k > 0 and Ω is...
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In this paper we study the existence, nonexistence and multiplicity of non-negative solutions for the family of problems −∆u = λ (a(x)e + f(x, u)), u ∈ H 0 (Ω) where Ω is a bounded domain in R2 and λ > 0 is a parameter. The coefficient a(x) is allowed to change sign. The techniques used in the proofs are a combination of upper and lower solutions, the TrudingerMoser inequality and variational m...
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ژورنال
عنوان ژورنال: ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE
سال: 2019
ISSN: 2036-2145,0391-173X
DOI: 10.2422/2036-2145.201609_001