Giampiero Palatucci

Local behavior of fractional p-minimizers

We extend the De Giorgi-Nash-Moser theory to nonlocal, possibly degenerate integro-differential operators.

A Singular Perturbation Result with a Fractional Norm

Let I be an open bounded interval of ℝ and W a non-negative continuous function vanishing only at α, β ∈ ℝ. We investigate the asymptotic behavior in terms of Γ-convergence of the following functional

p-Laplacian problems with critical Sobolev exponent

G_\varepsilon (u): = \varepsilon ^{p - 2} \iint_{I \times I} {\left| {\frac{{u(x) - u(y)}} {{x - y}}} \right|^p dxdy + \frac{1} {\varepsilon }\int_I {W(u)dx (p > 2),} }

Hitchhiker's guide to the fractional Sobolev spaces

, as ɛ → 0.

Existence and symmetry results for a Schrödinger type problem involving the fractional Laplacian

AbstractWe consider nonlinear parabolic equations of the type

Improved Sobolev embeddings, profile decomposition, and concentration-compactness for fractional Sobolev spaces

u_t - {\rm div}a(x, t, Du)= f(x, t) \quad {\rm on}\quad \Omega_T =\Omega\times (-T,0),