We obtain the existence of a 1-parameter family of nontrivial exterior domains Omega subset of RN which support a positive solution of Delta u=0in Omega,u=u0,partial derivative nu u=gamma H+C0on partial derivative Omega,limr ->+infinity u=0,if N >= 4 and Delta u=0in Omega,u=u0,partial derivative nu u=gamma K+C0on partial derivative Omega,limr ->+infinity u=+infinity,if N=2, where H is the mean curvature of partial derivative Omega,K is the curvature of partial derivative Omega, gamma is a parameter, u0 and C0 are constants. These domains bifurcates from the complement of a ball.
Bifurcation for an overdetermined boundary value problem in the complement of a ball in RN
Morabito F.
2025-01-01
Abstract
We obtain the existence of a 1-parameter family of nontrivial exterior domains Omega subset of RN which support a positive solution of Delta u=0in Omega,u=u0,partial derivative nu u=gamma H+C0on partial derivative Omega,limr ->+infinity u=0,if N >= 4 and Delta u=0in Omega,u=u0,partial derivative nu u=gamma K+C0on partial derivative Omega,limr ->+infinity u=+infinity,if N=2, where H is the mean curvature of partial derivative Omega,K is the curvature of partial derivative Omega, gamma is a parameter, u0 and C0 are constants. These domains bifurcates from the complement of a ball.File in questo prodotto:
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