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Bruno Pini Mathematical Analysis Seminar
ISSN 2240-2829 · University of Bologna · 158 artikel di indeks
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Artikel Jurnal
On the distance function in domains with boundary
We present some results on the regularity and the singularities of the distance function in domains with boundary.
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Artikel Jurnal
Correspondence Principle: A bridge between general potential theories and nonlinear elliptic differential operators
General potential theories concern the study of functions which are subharmonic with respect to a suitable constraint set $\cF$ in the space of 2-jets. While interesting in their own right, general potential theories are being widely used to study fully nonlinear PDEs determined by degenerate…
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Artikel Jurnal
Regularity results in elliptic and parabolic transmission problems
This paper surveys recent regularity results for transmission problems in both elliptic and parabolic settings. We also discuss the motivation behind these problems, illustrating them with concrete applications.
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Artikel Jurnal
Fully nonlinear equations with singular potentials in punctured balls
We present the results contained in [6,7], concerning radial solutions of fully nonlinear, uniformly elliptic equations posed in punctured balls, in presence of radial singular quadratic potentials. We discuss both the principal eigenvalues problem and the case of equations having also absorbing…
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On a long standing conjecture: positive Liouville Theorem for hypoelliptic Ornstein-Uhlenbeck operators
Let $\mathcal{L}$ be the hypoelliptic Ornstein-Uhlenbeck operator associated with the pair of matrices (A,B). In 2004, Priola and Zabczyk proved the following Liouville-type theorem: every bounded entire solution of $\mathcal{L}u=0$ is constant if and only if (*) every eigenvalue of B has real part…
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Artikel Jurnal
Semigroups generated by first order differential operators
The differentiation operator in a space of continuous or $L^p$ functions defined on an interval generates a translation semigroup. Here we illustrate the generalization of this result to general first-order operators, possibly singular.
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Artikel Jurnal
Liouville theorems for nonlocal operators with conical diffusion
We consider linear stable operators whose spectral measure is assumed to be positive only on a relatively open subset of the unit sphere, the aim being to present semilinear Liouville-type results for positive supersolutions in a half-space.
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Artikel Jurnal
On the propagation of isotropic Sobolev singularities
The aim of these notes is to examine the propagation of isotropic Sobolev (micro)singularities for an evolution problem whose generator is given by the Weyl quantization of a complex-valued quadratic form on phase space.
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Artikel Jurnal
Gradient regularity for strongly singular or degenerate elliptic and parabolic equations
We present recent advances in the regularity theory for weak solutions to some classes of elliptic and parabolic equations with strongly singular or degenerate structure. The equations under consideration satisfy standard $p$-growth and $p$-ellipticity conditions only outside a ball centered at the…
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Intrinsic regularity in homogeneous groups
We collect various results about the relations among the different notions of intrinsically regular submanifolds in homogeneous groups.
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Artikel Jurnal
On the characterization of the harmonic pseudospheres via Kuran’s functions and single-layer potentials
We present some characterizations of the harmonic pseudospheres in terms of the so called Kuran's functions and of the single-layer potentials. Our characterizations apply to solid, harmonically stable domains.
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Artikel Jurnal
Uniqueness results for variable coefficient Schrödinger equations
In this note we shall present some result proved in [16] on the uniqueness of Schrödinger equations with space-variable coefficients, that is Schrödinger equations where the Laplacian is replaced by an elliptic operator with space-variable coefficients.
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Exact controllability for nonlocal semilinear differential inclusions
In this paper, we investigate the controllability of a class of semilinear differential inclusions in Hilbert spaces. Assuming the exact controllability of the associated linear problem, we establish sufficient conditions for achieving the exact controllability of the nonlinear problem. In…
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Artikel Jurnal
Symmetry problems for gauge balls in the Heisenberg group
In this note we focus on possible characterizations of gauge-symmetric functions in the Heisenberg group. We discuss a family of inverse problems in potential theory relating solid and surface weighted mean-value formulas, and we show a partial solution to such problems. To this aim, we review a…
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Artikel Jurnal
Bourgain-Brezis’s duality argument for continuous primitives
In this note we collect some results in ℝn about global Poincaré inequalities for differential forms obtained in a joint research with Pierre Pansu and presented by the authors in two seminars held in Bologna respectively in 2023 and 2024. At the end of the note we comment some very new results…
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Artikel Jurnal
Intrinsic regular surfaces in Carnot groups
A Carnot group $G$ is a simply connected, nilpotent Lie group with stratified Lie algebra. Intrinsic regular surfaces in Carnot groups play the same role as C1 surfaces in Euclidean spaces. As in Euclidean spaces, intrinsic regular surfaces can be locally defined in different ways: e.g. as non…
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On a rigidity result for Kolmogorov-type operators
Let D be a bounded open subset of ℝN and let z0 be a point of D. Assume that the Newtonian potential of D is proportional outside D to the potential of a mass concentrated at z0. Then D is a Euclidean ball centred at z0. This theorem, proved by Aharonov, Schiffer and Zalcman in 1981, was extended…
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Coarsening phenomena in the network flow
In this short note we summarize recent results on the asymptotic behaviour of the network flow and we give indications of an expected coarsening-type behaviour for the network flow past singularities. The paper is complemented with a discussion on critical points and local minimizers of the length…
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Artikel Jurnal
Elliptic systems with bounded solutions and double phase functionals
We study boundedness of weak solutions to elliptic systems of partial differential equations in divergence form, under the so-called p,q growth conditions. Examples are obtained by writing the Euler system of some double phase functionals.
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survey on boundary regularity for the fractional p-Laplacian and its applications
We survey some recent regularity results for fractional p-Laplacian elliptic equations, especially focusing on pure and weighted boundary Hölder continuity of the solutions of related Dirichlet problems. Then, we present some applications of such results to general nonlinear elliptic equations of…