Sentence examples for bounded domain in a from inspiring English sources

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.

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.

where Ω is a bounded domain in a Carnot group G and L is the sub-Laplacian.

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.

end{aligned} (1.2) where Ω is a bounded domain in a complete smooth metric measure space ((M,langle,rangle,e^{-f},dnu )), V is a non-negative continuous function on M, and ρ is a weight function which is positive and continuous on M. For the eigenvalues of (1.2), we can give the following universal inequalities.

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 )).

The estimate for the (k+1 th eigenvalue of bounded domains in a Euclidean space improves an important inequality obtained recently by Cheng and Yang.

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]).