Related papers: Sharp Morrey regularity theory for a fourth order …
We prove sharp regularity estimates for solutions of obstacle type problems driven by a class of degenerate fully nonlinear operators; more specifically, we consider viscosity solutions of \[ |D u|^\gamma F(x, D^2u) = f(x)\chi_{\{u>\phi\}}…
This paper deals with the space-homogenous Landau equation with very soft potentials, including the Coulomb case. This nonlinear equation is of parabolic type with diffusion matrix given by the convolution product of the solution with the…
Motivated by applications to gas filtration problems, we study the regularity of weak solutions to the strongly degenerate parabolic PDE $u_{t}-\mathrm{div}\left((\vert Du\vert-\nu)_{+}^{p-1}\frac{Du}{\vert Du\vert}\right)=f$ in…
We first show the equivalence of two classes of generalized suitable weak solutions to the 3D incompressible Navier-Stokes equations allowing distributional pressure, the class of dissipative weak solutions and local suitable weak…
We prove well-posedness and higher-order regularity for a linear structurally damped plate equation with inhomogeneous Dirichlet--Neumann boundary conditions on the half-space and on bounded domains. To this end, we study maximal regularity…
In this work, we establish sharp and improved regularity estimates for viscosity solutions of Hardy-H\'{e}non-type equations with possibly singular weights and strong absorption governed by the $\infty$-Laplacian $$ \Delta_{\infty} u(x) =…
The aim of this paper is to consider the linear ultraparabolic equation with bounded and VMO coefficients $a_{ij} (z)$. Assume that the operator $L_0$ obtained by freezing the coefficients $a_{ij}(z)$ at any point ${z_0} \in {\mathbb{R}^{N…
We prove maximal Schauder regularity for solutions to elliptic systems and Cauchy problems, in the space $C_b(\mathbb{R}^d;\mathbb{R}^m)$ of bounded and continuous functions, associated to a class of nonautonomous weakly coupled…
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…
The paper deals with the second order regularity properties of the weak solutions $u\in W^{1,\phi}(\Omega, \real^n)$ } of systems of the form \begin{equation*}\label{equareg} -\dive A(x,\E u)=f, \end{equation*} in a bounded domain…
This paper establishes a comprehensive well-posedness and regularity theory for time-fractional stochastic partial differential equations on $\mathbb{R}^d$ driven by mixed Wiener--L\'evy noises. The equations feature a Caputo time…
We consider wave equations on Lorentzian manifolds in case of low regularity. We first extend the classical solution theory to prove global unique solvability of the Cauchy problem for distributional data and right hand side on smooth…
We establish existence results for a class of mixed anisotropic and nonlocal $p$-Laplace equation with singular nonlinearities. We consider both constant and variable singular exponents. Our argument is based on an approximation method. To…
A debate has appeared in the literature on loop quantum gravity and spin foams, over whether the secondary simplicity constraints, reducing the connection to be Levi-Civita, should imply the shape matching conditions, reducing twisted…
An approach to some "optimal" (more precisely, non-improvable) regularity of solutions of the thin film equation u_{t} = -\nabla \cdot(|u|^{n} \nabla \D u) in \ren \times \re_+, u(x,0)=u_0(x) in \re^N, where n in (0,2) is a fixed exponent,…
Let $\mathrm{X}=(X_{1},...,X_{q})$ be a family of real smooth vector fields satisfying H\"{o}mander's condition. The purpose of this paper is to establish gradient estimates in generalized Morrey spaces for weak solutions of the divergence…
It is shown both locally and globally that $L_t^{\infty}(L_x^{3,q})$ solutions to the three-dimensional Navier-Stokes equations are regular provided $q\not=\infty$. Here $L_x^{3,q}$, $0<q\leq\infty$, is an increasing scale of Lorentz spaces…
Combining the sharp isoperimetric inequality established by Z. Balogh and A. Krist\'aly [Math. Ann., in press, doi:10.1007/s00208-022-02380-1] with an anisotropic symmetrization argument, we establish sharp Morrey-Sobolev inequalities on…
We consider the problem of establishing nonlinear smoothing as a general feature of nonlinear dispersive equations, i.e. the improved regularity of the integral term in Duhamel's formula, with respect to the initial data and the…
We apply the theory of Lie symmetries in order to study a fourth-order $1+2$ evolutionary partial differential equation which has been proposed for the image processing noise reduction. In particular we determine the Lie point symmetries…