We prove that the normalized Steklov eigenvalues of a bounded domain in a complete Riemannian manifold are bounded above in terms of the inverse of the isoperimetric ratio of the domain.
This paper presents a new fictitious domain formulation for the solution of a strongly elliptic boundary value problem with Neumann boundary conditions for a bounded domain in a finite-dimensional Euclidean space with a smooth (possibly only Lipschitz) boundary.
Let G be a bounded domain in a complete hyperbolic space (left( X,dright) ) and suppose (f:overline{G}rightarrow X) is a nonexpansive mapping.
Let G be a bounded domain in a complete hyperbolic space (left( X,dright) ) and suppose (f:overline{G}rightarrow X) is either a Browder or a Geraghty (III) contraction.
From the Fourier transform method, the modified Green operator integral over a bounded domain in an infinite elastic medium takes, on each domain point, the form of a weighted average over an angular distribution of a single elementary operator.
Let Ω be a connected bounded domain in an n-dimensional complete smooth metric measure space ((M,langle,rangle, e^{-f},dnu )).
where is a bounded domain in with a smooth boundary, is a convex, real value function defined on, and denotes the derivative of.
Let be a an open bounded domain in, with a smooth boundary Let and where is a positive real number Then is smooth and any point on satisfies the inside (and outside) strong sphere property (see [1]).
where is a bounded domain in with a smooth boundary, and are real numbers, and is a divergence operator (degenerate Laplace operator) with, which is called a -Laplace operator.
