A priori bounds for solutions of a nonlocal evolution PDE

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Abstract

We obtain L∞ bounds, independent of ε for the equation (formula presented) Here, f is supposed to be constant outside a bounded interval and L is a suitable nonlocal operator, such as the fractional Laplacian.

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Caffarelli, L., & Valdinoci, E. (2013). A priori bounds for solutions of a nonlocal evolution PDE. In Springer INdAM Series (Vol. 4, pp. 141–163). Springer International Publishing. https://doi.org/10.1007/978-88-470-2592-9_10

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