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Elliptic Partial Differential Equation Involving a Singularity and a Radon Measure


Affiliations
1 Department of Mathematics, National Institute of Technology, Rourkela, India
     

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The aim of this paper is to prove the existence of solution for a partial differential equation involving a singularity with a general nonnegative, Radon measure μ as its nonhomogenous term which is given as

−Δu = f(x)h(u) + μ in Ω,

u = 0 on ∂Ω,

u > 0 on Ω,

where Ω is a bounded domain of RN, f is a nonnegative function over Ω.

Keywords

Elliptic PDE, Sobolev Space, Schauder Fixed Point Theorem
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  • Elliptic Partial Differential Equation Involving a Singularity and a Radon Measure

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Authors

Akasmika Panda
Department of Mathematics, National Institute of Technology, Rourkela, India
Sekhar Ghosh
Department of Mathematics, National Institute of Technology, Rourkela, India
Debajyoti Choudhuri
Department of Mathematics, National Institute of Technology, Rourkela, India

Abstract


The aim of this paper is to prove the existence of solution for a partial differential equation involving a singularity with a general nonnegative, Radon measure μ as its nonhomogenous term which is given as

−Δu = f(x)h(u) + μ in Ω,

u = 0 on ∂Ω,

u > 0 on Ω,

where Ω is a bounded domain of RN, f is a nonnegative function over Ω.

Keywords


Elliptic PDE, Sobolev Space, Schauder Fixed Point Theorem

References