56 research outputs found
Asymptotics for quasilinear obstacle problems in bad domains
We study two obstacle problems involving the p-Laplace operator in domains with n-th pre-fractal and fractal boundary. We perform asymptotic analysis for and
Delayed and rushed motions through time change
We introduce a definition of delayed and rushed processes in terms of
lifetimes of base processes and time-changed base processes. Then, we consider
time changes given by subordinators and their inverse processes. Our analysis
shows that, quite surprisingly, time-changing with inverse subordinators does
not necessarily imply delay of the base process. Moreover, time-changing with
subordinators does not necessarily imply rushed base process.Comment: to appear on ALEA - Latin American Journal of Probability and
Mathematical Statistic
Limit of p-Laplacian Obstacle problems
In this paper we study asymptotic behavior of solutions of obstacle problems
for Laplacians as For the one-dimensional case and for the
radial case, we give an explicit expression of the limit. In the n-dimensional
case, we provide sufficient conditions to assure the uniform convergence of
whole family of the solutions of obstacle problems either for data that
change sign in or for data (that do not change sign in )
possibly vanishing in a set of positive measure
Weighted Estimates on fractal domains
The aim of the paper is to establish estimates in weighted Sobolev
spaces for the solutions of the Dirichlet problems on snowflake domains, as well as uniform estimates for the solutions of the Dirichlet problems on pre-fractal approximating domains
Reinforcement problems for variational inequalities on fractal sets
The aim of this paper is to study reinforcement problems for variational inequalities of the obstacle type on fractal sets
Eikonal equations on the Sierpinski gasket
We study the eikonal equation on the Sierpinski gasket in the spirit of the
construction of the Laplacian in Kigami [8]: we consider graph eikonal
equations on the prefractals and we show that the solutions of these problems
converge to a function defined on the fractal set. We characterize this limit
function as the unique metric viscosity solution to the eikonal equation on the
Sierpinski gasket according to the definition introduced in [3]
Fractional Cauchy problem on random snowflakes
We consider time-changed Brownian motions on random Koch (pre-fractal and
fractal) domains where the time change is given by the inverse to a
subordinator. In particular, we study the fractional Cauchy problem with Robin
condition on the pre-fractal boundary obtaining asymptotic results for the
corresponding fractional diffusions with Robin, Neumann and Dirichlet boundary
conditions on the fractal domain
Nonlinear energy forms and Lipschitz spaces on the infinite Koch curve
We consider the nonlinear convex energy forms epsilon(K )((P)) on the infinite K- curve and we prove that the corresponding domains F-K ((p)) coincide with the spaces Lip(delta,df)(p, infinity, K-), where delta = log 3/log 4
Fractional Cauchy problem on random snowflakes
Abstract. We consider time-changed Brownian motions on random Koch (pre-fractal and fractal) domains where the time change is given by the inverse to a subordinator. In particular, we study the fractional Cauchy problem with Robin condition on the pre-fractal boundary obtaining asymptotic results for the corresponding fractional diffusions with Robin, Neumann and Dirichlet boundary conditions on the fractal domain
- …