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math.AP2025
The pinning effect of dilute defects
William M Feldman, Inwon C Kim
We consider the Bernoulli free boundary problem with ``defects", inhomogeneities in the coefficients of compact support. When the defects are small and arrayed periodically there e…
math.AP2025
Rate independent capillary motion on a narrow Wilhelmy plate
Carson Collins, William M Feldman
We study a rate independent energetic model of the Wilhelmy plate experiment in capillarity. The evolution is driven by vertical motions of the plate. We show stability of energy s…
math.AP2025
Compactness for via concentration-compactness
William M Feldman, Kerrek Stinson
Motivated by variational models for fracture, we provide a new proof of compactness for functions without a priori bounds on the function itself. Our proof is based on the…