Related papers: Maximal $L^q$-regularity for parabolic Hamilton-Ja…

We show in this paper that maximal $L^q$-regularity for time-dependent viscous Hamilton-Jacobi equations with unbounded right-hand side and superquadratic $\gamma$-growth in the gradient holds in the full range $ q >…

This paper studies a maximal $L^q$-regularity property for nonlinear elliptic equations of second order with a zero-th order term and gradient nonlinearities having superlinear and sub-quadratic growth, complemented with Dirichlet boundary…

We discuss quantitative Calder\'on-Zygmund estimates in $W^{2,2}$ for 2D viscous Hamilton-Jacobi equations with natural growth in the gradient. We apply the result to obtain the existence of classical solutions for stationary second order…

We investigate time-dependent mean-field games with superquadratic Hamiltonians and a power dependence on the measure. Such problems pose substantial mathematical challenges as the key techniques used in the subquadratic case do not extend…

For $q>2, \gamma > 1$, we prove that maximal regularity of $L^q$ type holds for periodic solutions to $-\Delta u + |Du|^\gamma = f$ in $\mathbb{R}^d$, under the (sharp) assumption $q > d \frac{\gamma-1}\gamma$.

We study a class of parabolic equations having first order terms with superlinear (and subquadratic) growth. The model problem is the so-called viscous Hamilton-Jacobi equation with superlinear Hamiltonian. We address the problem of having…

Viscosity solutions of fully nonlinear, local or non local, Hamilton-Jacobi equations with a super-quadratic growth in the gradient variable are proved to be H\"older continuous, with a modulus depending only on the growth of the…

We show that solutions of time-dependent degenerate parabolic equations with super-quadratic growth in the gradient variable and possibly unbounded right-hand side are locally ${\mathcal C}^{0,\alpha}$. Unlike the existing (and more…

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 determine the large-time behavior of unbounded solutions for the so-called viscous Hamilton Jacobi equation, $u_t - \Delta u + |Du|^m = f(x)$, in the quadratic and subquadratic cases (i.e., for $1<m\leq 2$), with a particular focus on…

In this paper we prove higher regularity for 2m-th order parabolic equations with general boundary conditions. This is a kind of maximal L_p-L_q regularity with differentiability, i.e. the main theorem is isomorphism between the solution…

We provide Lipschitz regularity for solutions to viscous time-dependent Hamilton-Jacobi equations with right-hand side belonging to Lebesgue spaces. Our approach is based on a duality method, and relies on the analysis of the regularity of…

In this paper, we prove the existence of classical solutions for time dependent mean-field games with a logarithmic nonlinearity and subquadratic Hamiltonians. Because the logarithm is unbounded from below, this nonlinearity poses…

In this note, we give an introduction to the concept of maximal $L^p$-regularity as a method to solve nonlinear partial differential equations. We first define maximal regularity for autonomous and non-autonomous problems and describe the…

We investigate the regularity of solutions of first order Hamilton-Jacobi equation with super linear growth in the gradient variable. We show that the solutions are locally H\"older continuous with H\"older exponent depending only on the…

We study the large-time behavior of bounded from below solutions of parabolic viscous Hamilton-Jacobi Equations in the whole space $\mathbb{R}^N$ in the case of superquadratic Hamiltonians. Existence and uniqueness of such solutions are…

This paper studies the time-inconsistent MV optimal stopping problem via a game-theoretic approach to find equilibrium strategies. To overcome the mathematical intractability of direct equilibrium analysis, we propose a vanishing…

It is well-known that solutions to the basic problem in the calculus of variations may fail to be Lipschitz continuous when the Lagrangian depends on t. Similarly, for viscosity solutions to time-dependent Hamilton-Jacobi equations one…

We prove stochastic homogenization for a class of non-convex and non-coercive first-order Hamilton-Jacobi equations in a finite-range-dependence environment for Hamiltonians that can be expressed by a max-min formula. Exploiting the…

In this paper we present an abstract maximal $L^p$-regularity result up to $T = \infty$, that is tuned to capture (linear) Partial Differential Equations of parabolic type, defined on a bounded domain and subject to finite dimensional,…