Related papers: Gradient Holder regularity for parabolic normalize…

We consider vector valued weak solutions $u:\Omega_T\to \mathbb{R}^N$ with $N\in \mathbb{N}$ of degenerate or singular parabolic systems of type \begin{equation*} \partial_t u - \mathrm{div} \, a(z,u,Du) = 0 \qquad\text{in}\qquad \Omega_T=…

In this paper we study the regularity of viscosity solutions to the following Hamilton-Jacobi equations $$ \partial_t u + H(D_{x} u)=0 \qquad \textrm{in} \Omega\subset \mathbb R\times \mathbb R^{n} . $$ In particular, under the assumption…

In this paper, we obtain a stochastic approximation that converges to the viscosity solution of the weighted $p$-Laplace equation. We consider a stochastic two-player zero-sum game controlled by a random walk, two player's choices, and the…

Let $u$ be the unique nonnegative viscosity solution of the Hamilton-Jacobi equation $H(x,\nabla u)=0$ in the external domain ${\mathbb R}^{ n} \setminus K$ with $u=0$ on $K$. Under general conditions on $H$, we prove that all sublevels of…

We obtain space-time H\"older regularity estimates for solutions of first- and second-order Hamilton-Jacobi equations perturbed with an additive stochastic forcing term. The bounds depend only on the growth of the Hamiltonian in the…

We prove existence and uniqueness of viscosity solutions to the degenerate parabolic problem $u_t = \Delta_\infty^h u$ where $\Delta_\infty^h$ is the $h$-homogeneous operator associated with the infinity-Laplacian, $\Delta_\infty^h u =…

We consider nonlinear parabolic equations of the type $$ u_t - div a(x, t, Du)= f(x,t) on \Omega_T = \Omega\times (-T,0), $$ under standard growth conditions on $a$, with $f$ only assumed to be integrable. We prove general decay estimates…

This paper investigates the relation between the boundary geometric properties and the boundary regularity of the solutions of elliptic equations. We prove by a new unified method the pointwise boundary H\"{o}lder regularity under proper…

We establish the interior $C^{1,\alpha}$-estimate for viscosity solutions of degenerate/singular fully nonlinear parabolic equations $$u_t = |Du|^{\gamma}F(D^2u) + f.$$ For this purpose, we prove the well-posedness of the regularized…

This paper is concerned with higher H\"older regularity for viscosity solutions to non-translation invariant second order integro-PDEs, compared to \cite{mou2018}. We first obtain $C^{1,\alpha}$ regularity estimates for fully nonlinear…

We prove regularity estimates for time derivatives of a large class of nonlinear parabolic partial differential systems. This includes the instationary (symmetric) p-Laplace system and models for non Newtonien fluids of powerlaw or Carreau…

In this paper we use probabilistic arguments (Tug-of-War games) to obtain existence of viscosity solutions to a parabolic problem of the form $$ {cases} K_{(x,t)}(D u)u_t (x,t)= \frac12 <D^2 u J_{(x,t)}(D u),J_{(x,t)}(D u) (x,t) &{in}…

In this manuscript, we study geometric regularity estimates for degenerate parabolic equations of $p$-Laplacian type ($2 \leq p< \infty$) under a strong absorption condition: $ \Delta_p u - \frac{\partial u}{\partial t} = \lambda_0 u_{+}^q…

We prove the intrinsic Harnack's inequality for a general form of a parabolic equation that generalizes both the standard parabolic $p$-Laplace equation and the normalized version arising from stochastic game theory. We prove each result…

This article establishes an interior gradient higher integrability result for weak solutions to parabolic multi-phase problems. The prototype equation for the parabolic multi-phase problem of $p$-Laplace type is given by \[ u_t -…

Let $(M^{n},g)$ be a complete Riemannian manifold. In this paper, we establish a space-time gradient estimates for positive solutions of nonlinear parabolic equations $$\partial_{t}u(x,t)=\Delta u(x,t)+a u(x,t)(\log u(x,t))^b +…

We study local regularity for nonlocal doubly degenerate parabolic equations. The model equation is \begin{equation*}\begin{split}…

In this paper we present the following result on regularity of solutions of the second order parabolic equation $\partial_t u - \mbox{div} (A \nabla u)+B\cdot \nabla u=0$ on cylindrical domains of the form $\Omega=\mathcal O\times\mathbb R$…

In this paper, we prove the stabilizability of abstract Parabolic Integro-Differential Equations (PIDE) in a Hilbert space with decay rate $e^{-\gamma t} $ for certain $\gamma > 0,$ by means of a finite dimensional controller in the…

In this paper, we obtain local H\"older regularity for bounded, weak solutions to the anisotropic $p$-Laplace equation whose prototype structure is given by $$ \sum_{i=1}^N (|u_{x_i}|^{p_i-2}u_{x_i})_{x_i}=0,$$ where $1 < p_1 \leq p_2 \leq…