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math.AP2026
Blow-up of solutions to semilinear parabolic equations driven by mixed local-nonlocal operators with large initial data
Stefano Biagi, Fabio Punzo, Eugenio Vecchi
We investigate finite-time blow-up for nonnegative solutions to the Cauchy problem associated with semilinear parabolic equations driven by a mixed local--nonlocal operator. The re…
math.AP2026
Existence and uniqueness of weak solutions to singular anisotropic elliptic problems
Francesco Esposito, Francescantonio Oliva, Eugenio Vecchi
In this paper we consider a quasilinear singular anisotropic elliptic problem with a p-sublinear perturbation. We prove uniqueness of weak solutions and we provide necessary and su…
math.AP2026
On a Sobolev critical problem for the superposition of a local and nonlocal operator with the "wrong sign''
Stefano Biagi, Serena Dipierro, Enrico Valdinoci +1
We study a critical problem for an operator of mixed order obtained by the superposition of a Laplacian with a fractional Laplacian. The main novelty is that we consider a mixed op…