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arXiv · 2510.02942

Non-bilinear Dirichlet Functionals: Markovianity, locality, invariance

Giovanni Brigati·Lorenzo Dello Schiavo
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Abstract

We present in a unified setting the foundations for a theory of non-bilinear Dirichlet functionals on Hilbert spaces. We prove known and new equivalences between non-linear semigroups, non-linear resolvents, non-linear generators, and their energy functionals, including a complete characterization of Markovianity. We introduce and characterize strong notions of invariance for general lower semicontinuous convex functionals, and notions of locality and strong locality for non-bilinear Dirichlet functionals. Contrary to many partial results in the literature, these characterizations are complete and correctly extend the analogous assertions for the bilinear case in full generality.

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Giovanni Brigati, Lorenzo Dello Schiavo. 2025-10-03. Non-bilinear Dirichlet Functionals: Markovianity, locality, invariance. https://arxiv.org/abs/2510.02942

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