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Reproducing Kernel for Neumann Boundary Conditions
Punjab University Journal of Mathematics, 2022We investigate a kernel space which is a particular class of Hilbert space. We discuss various properties of the reproducing kernel. In particular, our aim to construct kernel in reproducing space of the specific function space (Sobolev space) with the inner product and norm. Also, we derive the reproducing kernel for Neumann boundary conditions.
Gautam Patel, Kaushal Patel
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Roughness effect on Neumann boundary condition [PDF]
We study the effect of a periodic roughness on a Neumann boundary condition. We show that, as in the case of a Dirichlet boundary condition, it is possible to approach this condition by a more complex law on a domain without rugosity, called wall law. This approach is however different from that usually used in Dirichlet case.
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Estimates of Heat Kernels with Neumann Boundary Conditions
Potential Analysis, 2012This paper is concerned with two-sided estimates for the heat kernels corresponding to general elliptic operators of the form \(Lu=\frac{1}{2}\nabla\cdot(A\nabla u)+b\cdot \nabla u-\nabla(\hat bu)+qu\) in a bounded domain \(D\subset \mathbb R^N\) subject to Robin boundary conditions: \(\frac{1}{2}\langle A\nabla u,n\rangle-\langle \hat b,n\rangle u=0\)
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