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14 papers · 2 filters
The Zakharov system in dimension
Timothy Candy, Sebastian Herr, Kenji Nakanishi
The sharp range of Sobolev spaces is determined in which the Cauchy problem for the classical Zakharov system is well-posed, which includes existence of solutions, uniqueness, pers…
The Lipschitz truncation of functions of bounded variation
Dominic Breit, Lars Diening, Franz Gmeineder
We construct a Lipschitz truncation which approximates functions of bounded variation in the area-strict metric. The Lipschitz truncation changes the original function only on a sm…
Strong dissipativity of generalized time-fractional derivatives and quasi-linear (stochastic) partial differential equations
Wei Liu, Michael Röckner, José Luís da Silva
In this paper strong dissipativity of generalized time-fractional derivatives on Gelfand triples of properly in time weighted -path spaces is proved. In particular, the classi…
Asymptotics of fundamental solutions for time fractional equations with convolution kernels
Yury Kondratiev, Andrey Piatnitski, Elena Zhizhina
The paper deals with the large time asymptotic of the fundamental solution for a time fractional evolution equation for a convolution type operator. In this equation we use a Caput…
Schauder theorems for a class of (pseudo-)differential operators on finite and infinite dimensional state spaces
Alessandra Lunardi, Michael Röckner
We prove maximal regularity results in Hölder and Zygmund spaces for linear stationary and evolution equations driven by a large class of differential and pseudo-differential opera…
Local and global well-posedness of dispersion generalized Benjamin-Ono equations on the circle
Robert Schippa
New local well-posedness results for dispersion generalized Benjamin-Ono equations on the torus are proved. The family of equations under consideration links the Benjamin-Ono and K…