Abstract Let Ω⊂ ℝ N Ω⊂R^N be an arbitrary open set with boundary∂ Ω. Let p∈ 1,∞)
p∈1,∞) and s∈(0, 1). In the first part of the article we give some useful properties of the …

The main goal of this work is to study existence, uniqueness and summability of the solution
u with respect to the summability of the datum f. In the process we establish an Lp-theory, for …

We prove the W loc 2⁢ s, p local elliptic regularity of weak solutions to the Dirichlet problem
associated with the fractional Laplacian on an arbitrary bounded open set of ℝ N. The key …

We introduce a fractional variant of the Cahn–Hilliard equation settled in a bounded domain
Ω⊂ RN and complemented with homogeneous Dirichlet boundary conditions of solid type …

We consider the nonlinear problem (P)\qquad\left {I u= f (x, u) &\quad in\Omega,\u= 0 &\quad
on\mathbb R^ N ∖ Ω\.(P) I u= f (x, u) in Ω, u= 0 on RN\Ω in an open bounded set Ω ⊂ R^ N …

Abstract Very recently Warma (2019 SIAM J. Control Optim. to appear) has shown that for
nonlocal PDEs associated with the fractional Laplacian, the classical notion of controllability …

We investigate the monotonicity method for fractional semilinear elliptic equations with
power type nonlinearities. We prove that if-and-only-if monotonicity relations between …

We analyse the controllability problem for a one-dimensional heat equation involving the
fractional Laplacian on the interval. Using classical results and techniques, we show that …

We generalize many recent uniqueness results on the fractional Calderón problem to cover
the cases of all domains with nonempty exterior. The highlight of our work is the …

Let Ω⊂R^N be a bounded domain with a Lipschitz continuous boundary. We study the
controllability of the space-time fractional diffusive equation {\mathbbD_t^αu+ …