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Volume 7, Issue 2
Coercivity of the Single Layer Heat Potential

Douglas N. Arnold & Patrick J. Noon

J. Comp. Math., 7 (1989), pp. 100-104.

Published online: 1989-07

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  • Abstract

The single layer heat potential operator, K, arises in the solution of initial-boundary value problems for the heat equation using boundary integral methods. In this note we show that K maps a certain anisotropic Sobolev space isomorphically onto its dual, and, moreover, satisfies the coercivity inequality $ < K_{q,q} >\geq c\|q\|^2$. We thereby establish the well-posedness of the operator equation $K_q=f$ and provide a basis for the analysis of the discretizations.

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@Article{JCM-7-100, author = {Douglas N. Arnold and Patrick J. Noon}, title = {Coercivity of the Single Layer Heat Potential}, journal = {Journal of Computational Mathematics}, year = {1989}, volume = {7}, number = {2}, pages = {100--104}, abstract = {

The single layer heat potential operator, K, arises in the solution of initial-boundary value problems for the heat equation using boundary integral methods. In this note we show that K maps a certain anisotropic Sobolev space isomorphically onto its dual, and, moreover, satisfies the coercivity inequality $ < K_{q,q} >\geq c\|q\|^2$. We thereby establish the well-posedness of the operator equation $K_q=f$ and provide a basis for the analysis of the discretizations.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9459.html} }
TY - JOUR T1 - Coercivity of the Single Layer Heat Potential AU - Douglas N. Arnold & Patrick J. Noon JO - Journal of Computational Mathematics VL - 2 SP - 100 EP - 104 PY - 1989 DA - 1989/07 SN - 7 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9459.html KW - AB -

The single layer heat potential operator, K, arises in the solution of initial-boundary value problems for the heat equation using boundary integral methods. In this note we show that K maps a certain anisotropic Sobolev space isomorphically onto its dual, and, moreover, satisfies the coercivity inequality $ < K_{q,q} >\geq c\|q\|^2$. We thereby establish the well-posedness of the operator equation $K_q=f$ and provide a basis for the analysis of the discretizations.

Douglas N. Arnold and Patrick J. Noon. (1989). Coercivity of the Single Layer Heat Potential. Journal of Computational Mathematics. 7 (2). 100-104. doi:
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