We consider a shape optimization problem for the first mixed Steklov-Dirichlet eigenvalues of domains bounded by two balls in two-point homogeneous space. We give a geometric proof which is motivated by Newton's shell theorem
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4 results for “Steklov-Dirichlet”
The paper examines how the first Steklov-Dirichlet eigenvalue changes with the distance between two concentric circles.
problem Investigating the monotonicity of the first Steklov-Dirichlet eigenvalue on eccentric annuli.
method The approach involves showing differentiability, deriving integral expressions for the derivative, and using variational formulations to find upper and lower bounds.
result The paper proves the monotonicity of the first Steklov-Dirichlet eigenvalue on eccentric annuli with respect to the distance between the centers of the inner and outer boundaries.
Study on biharmonic Steklov problems with Neumann boundary conditions and eigenvalue estimates.
problem Biharmonic Steklov problems with Neumann boundary conditions.
method Introduced a biharmonic Steklov problem and proved its well-posedness. Established eigenvalue estimates using Kuttler-Sigillito inequalities.
result Eigenvalue estimates for the biharmonic Steklov problem with Neumann boundary conditions.
Lower bound for Steklov eigenvalues on negatively curved manifolds.
problem Finding a geometric lower bound for the first nonzero Steklov eigenvalue.
method Combining a uniform lower bound for the first eigenvalue of the Steklov-Dirichlet problem and a tubular neighborhood theorem for totally geodesic hypersurfaces.
result A geometric lower bound for the first nonzero Steklov eigenvalue in terms of total and boundary volumes.