44 research outputs found

    The Abresch-Gromoll inequality in a non-smooth setting

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    We prove that the Abresch-Gromoll inequality holds on infinitesimally Hilbertian CD(K,N) spaces in the same form as the one available on smooth Riemannian manifolds

    A non-smooth Brezis-Oswald uniqueness result

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    We classify the non-negative critical points in W01,p(Ω)W^{1,p}_0(\Omega) of J(v)=∫ΩH(Dv)−F(x,v) dx J(v)=\int_\Omega H(Dv)-F(x, v)\, dx where HH is convex and positively pp-homogeneous, while t↦∂tF(x,t)/tp−1t\mapsto \partial_tF(x, t)/t^{p-1} is non-increasing. Since HH may not be differentiable and FF has a one-sided growth condition, JJ is only l.s.c. on W01,p(Ω)W^{1,p}_0(\Omega). We employ a weak notion of critical point for non-smooth functionals, derive sufficient regularity of the latter without an Euler-Lagrange equation available and focus on the uniqueness part of the results in \cite{BO}, through a non-smooth Picone inequality.Comment: 30 pages, comments welcome

    Nonlocal problems at critical growth in contractible domains

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    We prove the existence of a positive solution for nonlocal problems involving the fractional Laplacian and a critical growth power nonlinearity when the equation is set in a suitable contractible domain.Comment: 17 page

    A note on global regularity for the weak solutions of fractional p-Laplacian equations

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    We consider a boundary value problem driven by the fractional p-Laplacian operator with a bounded reaction term. By means of barrier arguments, we prove H\"older regularity up to the boundary for the weak solutions, both in the singular (12) case.Comment: 7 pages, Conferenza tenuta al XXV Convegno Nazionale di Calcolo delle Variazioni, Levico 2--6 febbraio 201
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