Search results for " Pd"
showing 10 items of 651 documents
Determining a Random Schrödinger Operator : Both Potential and Source are Random
2020
We study an inverse scattering problem associated with a Schr\"odinger system where both the potential and source terms are random and unknown. The well-posedness of the forward scattering problem is first established in a proper sense. We then derive two unique recovery results in determining the rough strengths of the random source and the random potential, by using the corresponding far-field data. The first recovery result shows that a single realization of the passive scattering measurements uniquely recovers the rough strength of the random source. The second one shows that, by a single realization of the backscattering data, the rough strength of the random potential can be recovered…
Local regularity for time-dependent tug-of-war games with varying probabilities
2016
We study local regularity properties of value functions of time-dependent tug-of-war games. For games with constant probabilities we get local Lipschitz continuity. For more general games with probabilities depending on space and time we obtain H\"older and Harnack estimates. The games have a connection to the normalized $p(x,t)$-parabolic equation $(n+p(x,t))u_t=\Delta u+(p(x,t)-2) \Delta_{\infty}^N u$.
Resonances over a potential well in an island
2020
In this paper we study the distribution of scattering resonances for a multidimensional semi-classical Schr\"odinger operator, associated to a potential well in an island at energies close to the maximal one that limits the separation of the well and the surrounding sea.
Exact controllability to trajectories for entropy solutions to scalar conservation laws in several space dimensions
2019
We describe a new method which allows us to obtain a result of exact controllability to trajectories of multidimensional conservation laws in the context of entropy solutions and under a mere non-degeneracy assumption on the flux and a natural geometric condition.
Symmetry breaking in a constrained cheeger type isoperimetric inequality
2015
We study the optimal constant in a Sobolev inequality for BV functions with zero mean value and vanishing outside a bounded open set. We are interested in finding the best possible embedding constant in terms of the measure of the domain alone. We set up an optimal shape problem and we completely characterize the behavior of optimal domains.
Quasilinear Dirichlet Problems with Degenerated p-Laplacian and Convection Term
2021
The paper develops a sub-supersolution approach for quasilinear elliptic equations driven by degenerated p-Laplacian and containing a convection term. The presence of the degenerated operator forces a substantial change to the functional setting of previous works. The existence and location of solutions through a sub-supersolution is established. The abstract result is applied to find nontrivial, nonnegative and bounded solutions.
Convex functions on Carnot Groups
2007
We consider the definition and regularity properties of convex functions in Carnot groups. We show that various notions of convexity in the subelliptic setting that have appeared in the literature are equivalent. Our point of view is based on thinking of convex functions as subsolutions of homogeneous elliptic equations.
Monotonicity and enclosure methods for the p-Laplace equation
2018
We show that the convex hull of a monotone perturbation of a homogeneous background conductivity in the $p$-conductivity equation is determined by knowledge of the nonlinear Dirichlet-Neumann operator. We give two independent proofs, one of which is based on the monotonicity method and the other on the enclosure method. Our results are constructive and require no jump or smoothness properties on the conductivity perturbation or its support.
Enclosure method for the p-Laplace equation
2014
We study the enclosure method for the p-Calder\'on problem, which is a nonlinear generalization of the inverse conductivity problem due to Calder\'on that involves the p-Laplace equation. The method allows one to reconstruct the convex hull of an inclusion in the nonlinear model by using exponentially growing solutions introduced by Wolff. We justify this method for the penetrable obstacle case, where the inclusion is modelled as a jump in the conductivity. The result is based on a monotonicity inequality and the properties of the Wolff solutions.
Numerical Study of the semiclassical limit of the Davey-Stewartson II equations
2014
We present the first detailed numerical study of the semiclassical limit of the Davey–Stewartson II equations both for the focusing and the defocusing variant. We concentrate on rapidly decreasing initial data with a single hump. The formal limit of these equations for vanishing semiclassical parameter , the semiclassical equations, is numerically integrated up to the formation of a shock. The use of parallelized algorithms allows one to determine the critical time tc and the critical solution for these 2 + 1-dimensional shocks. It is shown that the solutions generically break in isolated points similarly to the case of the 1 + 1-dimensional cubic nonlinear Schrodinger equation, i.e., cubic…