Removable singularities of solutions of second-order parabolic equations
Copyright policy )Removable singularities of solutions of second-order parabolic equations
Let \({\mathcal L}\) denote a scalar linear second order parabolic operator on a bounded cylindrical domain \(Q\). Central in the paper is the notion of a set removable in a functional space \(Y\). By definition, it is a compact set \(E\subset Q\) such that if \(u\in Y\) is a weak solution of \({\mathcal L}u=0\) in \(Q\backslash E\) then necessarily \(u\equiv 0\) in \(Q\). A necessary and sufficient condition for a set to be removable in \(Y=V_ 2^{1,0}\) is established.
- Institute of Mathematics and Mechanics Azerbaijan
- Azerbaijan National Academy of Sciences Azerbaijan
Initial-boundary value problems for second-order parabolic equations, Smoothness and regularity of solutions to PDEs, scalar linear second order parabolic operator, weak solution, singularities, removable sets
Initial-boundary value problems for second-order parabolic equations, Smoothness and regularity of solutions to PDEs, scalar linear second order parabolic operator, weak solution, singularities, removable sets
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