A note on discontinuous problem with a free boundary

Journal of the Egyptian Mathematical Society

关键词: Variational inequalities;    Uniqueness;    Free boundary;   

DOI  :  10.1016/j.joems.2011.09.002

来源: DOAJ

【 摘 要 】

We study a nonlinear elliptic problem with discontinuous nonlinearity (P)-Δu=f(u)H(μ-u)inΩ,u=0on∂Ω, where H is the Heaviside’s unit function, f, h are given functions and μ is a positive real parameter. We prove the existence of a unique solution and characterize the corresponding free boundary. Our methods relies on variational inequality approach combining with fixed point arguments.

【 授权许可】

Unknown