ScratchPad Memories (SPMs) are commonly used in embedded systems because they are more energy-efficient than caches and enable tighter application control on the memory hierarchy. Optimally mapping code and data to SPMs is, however, still a challenge. This paper proposes an optimal scratchpad mapping approach for code segments, which has the distinctive… (More)
For a semilinear biharmonic Dirichlet problem in the ball with supercritical power-type nonlin-earity, we study existence/nonexistence, regularity and stability of radial positive minimal solutions. Moreover, qualitative properties, and in particular the precise asymptotic behaviour near x = 0 for (possibly existing) singular radial solutions, are deduced.… (More)
We prove some results about the first Steklov eigenvalue d 1 of the biharmonic operator in bounded domains. Firstly, we show that Fichera's principle of duality  may be extended to a wide class of nonsmooth domains. Next, we study the optimization of d1 for varying domains: we disprove a long-standing conjecture, we show some new and unexpected features… (More)
Asymptotics of solutions to Schrödinger equations with singular magnetic and electric potentials is investigated. By using a Almgren type monotonicity formula, separation of variables, and an iterative Brezis-Kato type procedure, we describe the exact behavior near the singularity of solutions to linear and semilinear (critical and subcritical) elliptic… (More)
We prove that minimizers for subcritical second order Sobolev embeddings in the unit ball are unique, positive and radially symmetric. Since the proofs of the corresponding first order results cannot be extended to the present situation we apply new and recently developed techniques.
We study existence and positivity properties for solutions of Cauchy problems for both linear and semilinear parabolic equations with the biharmonic operator as elliptic principal part. The self-similar kernel of the parabolic operator ∂ t + ∆ 2 is a sign changing function and the solution of the evolution problem with a positive initial datum may display… (More)
The biharmonic supercritical equation ∆ 2 u = |u| p−1 u, where n > 4 and p > (n + 4)/(n − 4), is studied in the whole space R n as well as in a modified form with λ(1 + u) p as right-hand-side with an additional eigenvalue parameter λ > 0 in the unit ball, in the latter case together with Dirichlet boundary conditions. As for entire regular radial solutions… (More)