Three Cylinder Inequalities and Unique Continuation Properties for Parabolic Equations (original) (raw)
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Acta Mathematica Sinica, English Series, 2005
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The authors consider the first boundary value problem for a second order parabolic equation with variable coefficients in a domain with conical points or edges. In the first part of the paper, they study the Green function for this problem in the domain K × R n-m , where K is an infinite cone in R m , 2 ≤ m ≤ n. They obtain the asymptotics of the Green function near the vertex (n = m) and edge (n > m), respectively. This result is applied in the second part of the paper, which deals with the initial-boundary value problem in this domain. Here, the right-hand side f of the differential equation belongs to a weighted L p space. At the end of the paper, the initial-boundary value problem in a bounded domain with conical points or edges is studied. http://www.boundaryvalueproblems.com/content/2014/1/252