Search results for "Equations"
showing 5 items of 955 documents
Hölder regularity for stochastic processes with bounded and measurable increments
2022
We obtain an asymptotic Hölder estimate for expectations of a quite general class of discrete stochastic processes. Such expectations can also be described as solutions to a dynamic programming principle or as solutions to discretized PDEs. The result, which is also generalized to functions satisfying Pucci-type inequalities for discrete extremal operators, is a counterpart to the Krylov-Safonov regularity result in PDEs. However, the discrete step size $\varepsilon$ has some crucial effects compared to the PDE setting. The proof combines analytic and probabilistic arguments.
On elliptic equations involving the 1-Laplacian operator
2018
El objetivo de esta tesis doctoral es dar a conocer los resultados obtenidos sobre existencia, unicidad y regularidad de las soluciones de diferentes ecuaciones elípticas regidas por el operador 1-laplaciano. El primer capítulo está dedicado al estudio de la ecuación - div (Du/|Du|) + g(u) |Du| = f(x) en un subconjunto abierto y acotado U de R^N con frontera Lipschitz, con la condición de Dirichlet u=0 en la frontera, tomando una función f positiva y siendo g una función real, continua y positiva. Por un lado, obtenemos soluciones no acotadas cuando el dato f pertenece al espacio de Marcinkiewicz L^{N,\infty}(U), por lo que debemos introducir la definición apropiada para este tipo de soluci…
Nonlinear evolution equations for turbulent superfluids
2010
In this paper a system of evolution equations for turbulent superfluid helium is written in the nonlinear regime, choosing as fundamental fields the density, the velocity, the heat flux, the non-equilibrium temperature and the average vortex line density per unit volume. Approximate equations are written, where second order terms in the non-equilibrium quantities are retained.
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.
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.