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 - <p style="text-align: justify;">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 $ &lt; K_{q,q} &gt;\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.</p>