Search results for "Solutions"
showing 7 items of 757 documents
PROGETTARE L’ADATTAMENTO. Resilienze di agricoltura urbana nel contesto europeo
2022
I crescenti fenomeni legati al cambiamento climatico spingono le città a sviluppare piani di resilienza che possano rispondere in termini di sostenibilità ambientale, sociale ed economica. Le strategie nature-based possono rappresentare una soluzione; tra queste l’agricoltura urbana può contribuire ad aumentare la resilienza dei tessuti urbani europei. Questa attività è stata più volte oggetto di interesse in periodi di crisi come impegno comunitario dai caratteri sociali, oltre che produttivi ed educativi. Attraverso un excursus storico e una successiva analisi di casi studio contemporanei, il paper fornisce strumenti progettuali per intervenire nel costruito con strategie che spaziano dal…
Hölder regularity for the gradient of the inhomogeneous parabolic normalized p-Laplacian
2018
In this paper, we study an evolution equation involving the normalized [Formula: see text]-Laplacian and a bounded continuous source term. The normalized [Formula: see text]-Laplacian is in non-divergence form and arises for example from stochastic tug-of-war games with noise. We prove local [Formula: see text] regularity for the spatial gradient of the viscosity solutions. The proof is based on an improvement of flatness and proceeds by iteration.
Regularity for nonlinear stochastic games
2015
We establish regularity for functions satisfying a dynamic programming equation, which may arise for example from stochastic games or discretization schemes. Our results can also be utilized in obtaining regularity and existence results for the corresponding partial differential equations. peerReviewed
Remarks on regularity for p-Laplacian type equations in non-divergence form
2018
We study a singular or degenerate equation in non-divergence form modeled by the $p$-Laplacian, $$-|Du|^\gamma\left(\Delta u+(p-2)\Delta_\infty^N u\right)=f\ \ \ \ \text{in}\ \ \ \Omega.$$ We investigate local $C^{1,\alpha}$ regularity of viscosity solutions in the full range $\gamma>-1$ and $p>1$, and provide local $W^{2,2}$ estimates in the restricted cases where $p$ is close to 2 and $\gamma$ is close to 0.
First and second order rational solutions to the Johnson equation and rogue waves
2018
Rational solutions to the Johnson equation are constructed as a quotient of two polynomials in x, y and t depending on several real parameters. We obtain an infinite hierarchy of rational solutions written in terms of polynomials of degrees 2N (N + 1) in x, and t, 4N (N + 1) in y, depending on 2N − 2 real parameters for each positive integer N. We construct explicit expressions of the solutions in the cases N = 1 and N = 2 which are given in the following. We study the evolution of the solutions by constructing the patterns of their modulus in the (x, y) plane, and this for different values of parameters.
Solutions to the Gardner equation with multi-parameters and the rational case
2022
We construct solutions to the Gardner equation in terms of trigonometric and hyperbolic functions, depending on several real parameters. Using a passage to the limit when one of these parameters goes to 0, we get, for each positive integer N , rational solutions as a quotient of polynomials in x and t depending on 2N parameters. We construct explicit expressions of these rational solutions for orders N = 1 until N = 3. We easily deduce solutions to the mKdV equation in terms of wronskians as well as rational solutions depending on 2N real parameters.
Properties of zeros of solutions to third order nonlinear differential equations
2013
We investigate the behavior of zeros of solutions to the certain type of third order nonlinear differential equations. We show that the behavior of zeros may be rather different and depend on the nature of nonlinearity in the equation. Main results in the paper are illustrated with a number of examples.