Related papers: H\"older continuity for the $p$-Laplace equation u…

We study the regularity of the $p$-Poisson equation $$ \Delta_p u = h, \quad h\in L^q $$ in the plane. In the case $p>2$ and $2<q<\infty$ we obtain the sharp H\"older exponent for the gradient. In the other cases we come arbitrarily close…

For the following Neumann problem in a ball $$\begin{cases} -\Delta_p u+u^{p-1}=u^{q-1}\quad&\text{in }B,\\ u>0,\,u\text{ radial}\quad&\text{in }B,\\ \frac{\partial u}{\partial \nu}=0\quad&\text{on }\partial B, \end{cases}$$ with…

We analyze $p$-Laplace operators with degenerate elliptic coefficients. This investigation includes Gru\v{s}in type $p$-Laplace operators. We describe a \emph{separation phenomenon} in elliptic and parabolic $p$-Laplace type equations,…

We are concerned with the problem of determining the nonlinear term in a semilinear elliptic equation by boundary measurements. Precisely, we improve [5, Theorem 1.3], where a logarithmic type stability estimate was proved. We show actually…

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 the H\"older continuity for weak solutions to parabolic p-Laplace equations on the Heisenberg group. We deduce this result while considering an optimal tail condition.

In this article we investigate the temporal regularity of strong solutions to the stochastic $p$-\com{L}aplace system in the degenerate setting, $p \in [2,\infty)$, driven by a multiplicative nonlinear stochastic forcing. We establish $1/2$…

In this work we consider the Neumann problem for the Laplace operator and we prove an existence result in the H\"older spaces and obtain Schauder estimates. According to our knowledge this result is not explicitly proved in the several…

We prove global existence, uniqueness and stability of entropy solutions with $L^2\cap L^\infty$ initial data for a general family of negative order dispersive equations. It is further demonstrated that this solution concept extends in a…

We show that the new result on H\"older continuity of solutions to a class of nondiagonal elliptic systems with $p$-growth in [2] can be used to improve the $L^q$ theory for such systems.

We study the Dirichlet problem for the complex Monge-Amp\`ere equation on a strictly pseudoconvex domain in Cn or a Hermitian manifold. Under the condition that the right-hand side lies in Lp function and the boundary data are H\"older…

We characterize removable sets for H\"older continuous solutions to degenerate parabolic equations of $p$-growth. A sufficient and necessary condition for a set to be removable is given in terms of an intrinsic parabolic Hausdorff measure,…

We study if two different solutions of the $p$-Laplace equation $$\nabla\cdot(|\nabla u|^{p-2}\nabla u)=0,$$ where $1<p<\infty$, can coincide in an open subset of their common domain of definition. We obtain some partial results on this…

Given any solution $u$ of the Euler equations which is assumed to have some regularity in space - in terms of Besov norms, natural in this context - we show by interpolation methods that it enjoys a corresponding regularity in time and that…

We show that local weak solutions to parabolic systems of p-Laplace type are H{\"o}lder continuous in time with values in a spatial Lebesgue space and H{\"o}lder continuous on almost every time line. We provide an elementary and…

In this paper, we examine the regularity of the solutions to the double-divergence equation. We establish improved H\"older continuity as solutions approach their zero level-sets. In fact, we prove that $\alpha$-H\"older continuous…

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 consider a combination of local and nonlocal $p$-Laplace equations and discuss several regularity properties of weak solutions. More precisely, we establish local boundedness of weak subsolutions, local H\"older continuity of weak…

We shall establish the interior H\"older continuity for locally bounded weak solutions to a class of parabolic singular equations whose prototypes are \begin{equation} u_t= \nabla \cdot \bigg( |\nabla u|^{p-2} \nabla u \bigg), \quad \text{…

We investigate the monotonicity of the minimal period of periodic solutions of quasilinear differential equations involving the $p$-Laplace operator. First, the monotonicity of the period is obtained as a function of a Hamiltonian energy in…