2014/12/23 by Moritz Kaßmann, Kassmann, Moritz, Ante Mimica +1
Computer Science · Mathematics · #31B05 #35B65 #35R09 #47G20 #60J75 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.1412.7566
openalex publication_date 2014/12/23 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We study integrodifferential operators and regularity estimates for solutions to integrodifferential equations. Our emphasis is on kernels with a critically low singularity which does not allow for standard scaling. For example, we treat operators that have a logarithmic order of differentiability. For corresponding equations we prove a growth lemma and derive a priori estimates. We derive these estimates by classical methods developed for partial differential operators. Since the integrodifferential operators under consideration generate Markov jump processes, we are able to offer an alternative approach using probabilistic techniques.