Abstract Quasilinear Parabolic Equations.
Schauder theorems for linear elliptic and parabolic problems with unbounded coefficients in
We study existence, uniqueness, and smoothing properties of the solutions to a class of linear second order elliptic and parabolic differential equations with unbounded coefficients in . The main results are global Schauder estimates, which hold in spite of the unboundedness of the coefficients.
Schauder estimates for a class of degenerate elliptic and parabolic operators with unbounded coefficients in
On optimal regularity in evolution equations
Using interpolation techniques we prove an optimal regularity theorem for the convolution , where is a strongly continuous semigroup in general Banach space. In the case of abstract parabolic problems – that is, when is an analytic semigroup – it lets us recover in a unified way previous regularity results. It may be applied also to some non analytic semigroups, such as the realization of the Ornstein-Uhlenbeck semigroup in , , in which case it yields new optimal regularity results in fractional...
Analyticity of the maximal solution of an abstract parabolic equation
Studia l’analiticità della soluzione massimale di una equazione parabolica astratta in spazi di Banach.
Characterization of some interpolation spaces (II)
Si caratterizzano alcuni spazi di interpolazione tra spazi di funzioni continue e domini di operatori ellittici del 2° ordine.
Characterization of some interpolation spaces (I)
Si calcolano alcuni spazi di interpolazione fra spazi di funzioni hölderiane.
Analyticity of the maximal solution of an abstract parabolic equation
Studia l’analiticità della soluzione massimale di una equazione parabolica astratta in spazi di Banach.
Characterization of some interpolation spaces (I)
Si calcolano alcuni spazi di interpolazione fra spazi di funzioni hölderiane.
Characterization of some interpolation spaces (II)
Si caratterizzano alcuni spazi di interpolazione tra spazi di funzioni continue e domini di operatori ellittici del 2° ordine.
Problemi parabolici a frontiera libera
Fully Nonlinear Integrodifferential Equations in General Banach Space.
Hopf bifurcation for fully nonlinear equations in Banach space
On a class of elliptic operators with unbounded coefficients in convex domains
We study the realization of the operator in , where is a possibly unbounded convex open set in , is a convex unbounded function such that and , is the element with minimal norm in the subdifferential of at , and is a probability measure, infinitesimally invariant for . We show that , with domain is a dissipative self-adjoint operator in . Note that the functions in the domain of do not satisfy any particular boundary condition. Log-Sobolev and Poincaré inequalities allow...
Maximal regularity for stochastic convolutions in spaces
We prove an optimal regularity result for stochastic convolutions in certain Banach spaces. It is stated in terms of real interpolation spaces.
Computation of bifurcated branches in a free boundary problem arising in combustion theory
Computation of bifurcated branches in a free boundary problem arising in combustion theory
We consider a parabolic Free Boundary Problem, with jump conditions at the interface. Its planar travelling-wave solutions are orbitally stable provided the bifurcation parameter does not exceed a critical value . The latter is the limit of a decreasing sequence of bifurcation points. The paper deals with the study of the bifurcated branches from the planar branch, for small . Our technique is based on the elimination of the unknown front, turning the problem into a one, to which...
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