We thank Dimitris Politis and Mohsen Pourahmadi for sharing their work and thoughts. The constructive comments of the four Referees and the Associate Editor is gratefully acknowledged. We thank the Editor for his encouragement to submit a revision.
Throughout this section uε is a nonzero weak solution of \rm div(A(x/ε)∇uε)=0 in B2 for some A∈A(λ,M). In view of Theorem 3.3 we assume that uε satisfies the doubling condition,
Although the contraction mapping theorem generally provides Lipschitz dependence on initial data for free, the above argument does not. This is because all of the linear propagators used in the proof of Theorem 2 depend on the initial data itself an…
It is well-known that local expansions of layer potentials are analytic away from the boundary. There are surprisingly few results in the literature, however, concerning the behavior of such expansions when evaluated at the limit of their radii of c…
We considered the problem of characterizing the loss surface of neural networks from the perspective of optimization, with the goal of deriving weak certificates that enable the existence of descent paths towards global minima.
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