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math.AP2026
Maximization of the efficiency of the first Dirichlet eigenfunction and improved eigenvalue inequalities
Francesco Della Pietra
We study the efficiency of the first Dirichlet eigenfunction on bounded convex domains , defined as the ratio between the mean value of on and it…
math.AP2025
Weighted Robin eigenvalue problems and nonlinear elliptic equations with general growth in the gradient
Francesco Della Pietra, Giuseppina di Blasio, Giuseppe Riey
We prove an existence result for Robin boundary value problems modeled on \[ \begin{cases} Δu + |\nabla u|^2 + λf(x) = 0 & \text{in } Ω \\ \frac{\partial u}{\partial ν} + βu = 0 &…
math.AP2024
Existence and regularity results for a class of non-uniformly elliptic Robin problems
Francesco Della Pietra, Giuseppina di Blasio, Teresa Radice
In this paper, we study the existence and the summability of solutions to a Robin boundary value problem whose prototype is the following: $$ \begin{cases} -\text{div}(b(|u|)\nabla…