Zobrazeno 1 - 10
of 183
pro vyhledávání: '"Magnanini, Rolando"'
We prove a new general differential identity and an associated integral identity, which entails a pair of solutions of the Poisson equation with constant source term. This generalizes a formula that the first and third authors previously proved and u
Externí odkaz:
http://arxiv.org/abs/2402.02845
Starting from a characterization of holomorphic functions in terms of a suitable mean value property, we build some nonlinear asymptotic characterizations for complex-valued solutions of certain nonlinear systems, which have to do with the classical
Externí odkaz:
http://arxiv.org/abs/2306.08437
We prove an existence result for the Backus interior problem in the Euclidean ball. The problem consists in determining a harmonic function in the ball from the knowledge of the modulus of its gradient on the boundary. The problem is severely nonline
Externí odkaz:
http://arxiv.org/abs/2212.00413
Autor:
Magnanini, Rolando, Poggesi, Giorgio
We consider a mixed boundary value problem in a domain $\Omega$ contained in a half-ball $B_+$ and having a portion $\bar{T}$ of its boundary in common with the curved part of $\partial B_+$. The problem has to do with some sort of constrained torsio
Externí odkaz:
http://arxiv.org/abs/2210.10288
Autor:
Magnanini, Rolando
We present a method to obtain explicit solutions of the complex eikonal equation in the plane. This equation arises in the approximation of Helmholtz equation by the WKBJ or EWT methods. We obtain the complex-valued solutions (called eikonals) as par
Externí odkaz:
http://arxiv.org/abs/2111.10852
Autor:
Magnanini, Rolando, Poggesi, Giorgio
We prove interpolating estimates providing a bound for the oscillation of a function in terms of two $L^p$ norms of its gradient. They are based on a pointwise bound of a function on cones in terms of the Riesz potential of its gradient. The estimate
Externí odkaz:
http://arxiv.org/abs/2109.02876
We consider Backus's problem in geophysics. This consists in reconstructing a harmonic potential outside the Earth when the intensity of the related field is measured on the Earth's surface. Thus, the boundary condition is (severely) nonlinear. The g
Externí odkaz:
http://arxiv.org/abs/2108.12077
In a recent paper, the last three authors showed that a game-theoretic $p$-harmonic function $v$ is characterized by an asymptotic mean value property with respect to a kind of mean value $\nu_p^r[v](x)$ defined variationally on balls $B_r(x)$. In th
Externí odkaz:
http://arxiv.org/abs/2101.02662
Publikováno v:
In Journal of Differential Equations 5 February 2024 381:20-47
Autor:
Magnanini, Rolando, Poggesi, Giorgio
In a domain of the Euclidean space, we estimate from below the distance to the boundary of global maximum points of solutions of elliptic and parabolic equations with homogeneous Dirichlet boundary values. As reference cases, we first consider the to
Externí odkaz:
http://arxiv.org/abs/2005.13175