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math.AP2025
Introduction to quantitative De Giorgi methods
Giovanni Brigati, Clément Mouhot
The theory of De Giorgi (1958) and Nash (1959) solves Hilbert's 19th problem and constitutes a major advance in the analysis of PDEs in the 20th century. This theory concerns the H…
math.FA2025
Non-linear Dirichlet Functionals: Markovianity, Locality, Invariance
Giovanni Brigati, Lorenzo Dello Schiavo
We present in a unified setting the foundations for a theory of non-linear Dirichlet functionals on Hilbert spaces. We prove known and new equivalences between non-linear semigroup…