Related papers: The Neumann problem for fully nonlinear SPDE
The aim of this work is to study the Navier-Stokes-Voigt equations that govern flows with non-negative density of incompressible fluids with elastic properties. For the associated non-linear initial-and boundary-value problem, we prove the…
Within the framework of variational modelling we derive a one-phase moving boundary problem describing the motion of a semipermeable membrane enclosing a viscous liquid, driven by osmotic pressure and surface tension of the membrane. For…
The results of the author and Gess [27] develop a robust well-posedness theory for a broad class of conservative stochastic PDEs, with both probabilistically stationary and non-stationary Stratonovich noise, and with irregular noise…
We investigate the pathwise well-posedness of stochastic evolution equations perturbed by multiplicative Neumann boundary noise, such as fractional Brownian motion for $H\in(1/3,1/2]$. Combining the controlled rough path approach with the…
We study the Cauchy problem for Schr\"odinger type stochastic partial differential equations with uniformly bounded coefficients on a curved space. We give conditions on the coefficients, on the drift and diffusion terms, on the Cauchy…
In this paper we study a non-homogeneous Neumann problem, where the $p(x)$-Laplacian is involved and $p=\infty$ in a subdomain. By considering a suitable sequence $p_k$ of bounded variable exponents such that $p_k \to p$ and replacing $p$…
In this paper we develop a new approach to nonlinear stochastic partial differential equations with Gaussian noise. Our aim is to provide an abstract framework which is applicable to a large class of SPDEs and includes many important cases…
We study the $\overline{\partial}$-Neumann problem using the Sobolev space inner product. We show that the problem can be solved on any smoothly bounded, pseudoconvex domain. We further formulate estimates and the basic results of a Sobolev…
We prove the unique solvability in weighted Sobolev spaces of non-divergence form elliptic and parabolic equations on a half space with the homogeneous Neumann boundary condition. All the leading coefficients are assumed to be only…
The celebrated De Giorgi-Nash-Moser theory ensures that solutions to uniformly elliptic or parabolic PDEs are bounded and H\"older continuous, even with merely bounded measurable coefficients. For parabolic SPDEs with transport noise,…
In this note, we discuss a poorly known alternative boundary condition to the usual Neumann or `stress-free' boundary condition typically used to weaken boundary layers when diffusion is present but very small. These `diffusion-free'…
We give meaning to linear and semi-linear (possibly degenerate) parabolic partial differential equations with (affine) linear rough path noise and establish stability in a rough path metric. In the case of enhanced Brownian motion (Brownian…
In this preprint we consider fully nonlinear equations in thin domains with oblique boundary condition, finding some new phenomena, in particular the limit equation contains "new terms" of the second, first and zeroth order which don't have…
We prove a regularization by noise phenomenon for semilinear SPDEs driven by multiplicative cylindrical Brownian motion and singular diffusion coefficient. The analysis is based on a combination of infinite dimensional generalizations of…
This paper is devoted to the study of hyperbolic systems of linear partial differential equations perturbed by a Brownian motion. The existence and uniqueness of solutions are proved by an energy method. The specific features of this class…
We introduce a new definition of viscosity solution to path-dependent partial differential equations, which is a slight modification of the definition introduced in [8]. With the new definition, we prove the two important results till now…
The purpose of this paper is to establish the well-posedness of the stochastic Stefan problem on moving hypersurfaces. Through a specially designed transformation, it turns out we need to solve stochastic partial differential equations on a…
We provide existence and uniqueness of global (and local) mild solutions for a general class of semilinear stochastic partial differential equations driven by Wiener processes and Poisson random measures under local Lipschitz and linear…
In this paper we investigate the non-linear and ill-posed inverse problem of simultaneously identifying the conductivity and the reaction in diffuse optical tomography with noisy measurement data available on an accessible part of the…
Stochastic partial differential equations (SPDEs) have become a key modelling tool in applications. Yet, there are many classes of SPDEs, where the existence and regularity theory for solutions is not completely developed. Here we…