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math.AP2015★ 16 cited
Boundedness of single layer potentials associated to divergence form parabolic equations with complex coefficients
Alejandro J. Castro, Kaj Nyström, Olow Sande
We consider parabolic operators of the form $$\partial_t+\mathcal{L},\ \mathcal{L}:=-\mbox{div}\, A(X,t)\nabla,$$ in $\mathbb R_+^{n+2}:=\{(X,t)=(x,x_{n+1},t)\in \mathbb R^{n}\time…
math.AP2015★ 9 cited
Solvability of the Dirichlet, Neumann and the regularity problems for parabolic equations with Hölder continuous coefficients
Alejandro J. Castro, Salvador Rodríguez-López, Wolfgang Staubach
We establish the -solvability of Dirichlet, Neumann and regularity problems for divergence-form heat (or diffusion) equations with Hölder-continuous diffusion coefficients, on…