On the Regularity of Minimal Surfaces with Free Boundaries in Riemannian Manifolds.
On the regularity of solutions in Convex Integration theory.
On the regularity of solutions of a thermoelastic system under noncontinuous heating regimes. II
A quasilinear noncoupled thermoelastic system is studied both on a threedimensional bounded domain with a smooth boundary and for a generalized model involving the influence of supports. Sufficient conditions are derived under which the stresses are bounded and continuous on the closure of the domain.
On the regularity of solutions of a thermoelastic system under noncontinuous heating regimes. III
In this part we weaken the sufficient condition to obtain the stresses continuous and bounded in the threedimensional case, and we treat a certain coupled system.
On the regularity of the stationary Navier-Stokes equations
On the regularity of the variational solution of the Tricomi problem in the elliptic region
On the regularity of the weak solution of Cauchy problem for nonlinear parabolic systems via Liouville property
On the regularity of weak solutions to nonlinear elliptic systems via Liouville's type property
On the regularity up to the boundary for higher order quasilinear elliptic systems
On the Riemann-Hilbert problem in the domain with a nonsmooth boundary.
On the rigidity of minimal mass solutions to the focusing mass-critical NLS for rough initial data.
On the role of the equal-area condition in internal layer stationary solutions to a class of reaction-diffusion systems.
On the scattering in Gevrey classes for the subcritical Hartree and Schrödinger equations
On the Schauder estimates of solutions to parabolic equations
On the Schrödinger equation in L...spaces.
On the Schrödinger heat kernel in horn-shaped domains
We prove pointwise lower bounds for the heat kernel of Schrödinger semigroups on Euclidean domains under Dirichlet boundary conditions. The bounds take into account non-Gaussian corrections for the kernel due to the geometry of the domain. The results are applied to prove a general lower bound for the Schrödinger heat kernel in horn-shaped domains without assuming intrinsic ultracontractivity for the free heat semigroup.
On the second order derivatives of convex functions on the Heisenberg group
In the euclidean setting the celebrated Aleksandrov-Busemann-Feller theorem states that convex functions are a.e. twice differentiable. In this paper we prove that a similar result holds in the Heisenberg group, by showing that every continuous –convex function belongs to the class of functions whose second order horizontal distributional derivatives are Radon measures. Together with a recent result by Ambrosio and Magnani, this proves the existence a.e. of second order horizontal derivatives for...
On the set of solutions of some nonconvex nonclosed hyperbolic differential inclusions
We consider a class of nonconvex and nonclosed hyperbolic differential inclusions and we prove the arcwise connectedness of the solution set.
On the sets of regularity of solutions for a class of degenerate nonlinear elliptic fourth-order equations with data.
On the short time asymptotic of the stochastic Allen–Cahn equation
A description of the short time behavior of solutions of the Allen–Cahn equation with a smoothened additive noise is presented. The key result is that in the sharp interface limit solutions move according to motion by mean curvature with an additional stochastic forcing. This extends a similar result of Funaki [Acta Math. Sin (Engl. Ser.)15 (1999) 407–438] in spatial dimension n=2 to arbitrary dimensions.