Related papers: Pointwise weak existence for diffusions associated…

In this paper we use variational methods to establish the existence of solutions for a class of nonlinear elliptic problems involving a combined convolution-type and Hardy nonlinearity with subcritical and critical growth.

We establish sufficient conditions for the local boundedness of weak solutions to a broad class of nonlinear elliptic equations in divergence form, under unbalanced growth conditions on the stress field. Our analysis is carried out in a…

We show uniqueness in law for a general class of stochastic differential equations in $\mathbb{R}^d$, $d\ge 2$, with possibly degenerate and/or fully discontinuous locally bounded coefficients among all weak solutions that spend zero time…

In this paper we study existence and spectral properties for weak solutions of Neumann and Dirichlet problems associated to second order linear degenerate elliptic partial differential operators $X$, with rough coefficients of the form…

In this paper, we investigate the existence of weak solutions for a class of degenerate elliptic Dirichlet problems with critical nonlinearity and a logarithmic perturbation

In this study, we devote our attention to the question of clarifying the existence of a weak solution to a class of quasilinear double-phase elliptic equations with logarithmic convection terms under some appropriate assumptions on data.…

We study the Dirichlet problem for a second order linear elliptic equation in a bounded smooth domain $\Omega$ in $\mathbb{R}^n$, $n \ge 3$, with the drift $\mathbf{b} $ belonging to the critical weak space $L^{n,\infty}(\Omega )$. We…

We present a proof for the existence and uniqueness of weak solutions for a cut-off and non cut-off model of non-linear diffusion equation in finite-dimensional space RD useful for modelling flows on porous medium with saturation, turbulent…

We study a class of partial differential equations in divergence form that admit highly irregular Lipschitz weak solutions. By reformulating these divergence-form equations as a first-order partial differential relation and adapting the…

Using a method developped in [1] and [2], we prove the existence of weak non trivial solutions to fourth order elliptic equations with singularities and with critical Sobolev growth.

We introduce a new extragradient iterative process, motivated and inspired by [S. H. Khan, A Picard-Mann Hybrid Iterative Process, Fixed Point Theory and Applications, doi:10.1186/1687-1812-2013-69], for finding a common element of the set…

Consider a class of non-homogenous ultraparabolic differential equations with drift terms or lower order terms arising from some physical models, and we prove that weak solutions are H\"{o}lder continuous, which also generalizes the classic…

We consider the two-dimensional incompressible inhomogeneous Navier-Stokes equations with odd viscosity, where the shear and the odd viscosity coefficients depend continuously on the unknown density function. We establish the existence of…

Chemical and biochemical reactions can exhibit surprisingly different behaviours, ranging from multiple steady-state solutions to oscillatory solutions and chaotic behaviours. These types of systems are often modelled by a system of…

We consider the stochastic continuity equation associated to an It\^{o} diffusion with irregular drift and diffusion coefficients. We give regularity conditions under which weak solutions are renormalized in the sense of DiPerna/Lions, and…

A class of (possibly) degenerate integro-differential equations of parabolic type is considered, which includes the Kolmogorov equations for jump diffusions. Existence and uniqueness of the solutions are established in Bessel potential…

In this paper, we study the averaging principle for distribution dependent stochastic differential equations with drift in localized $L^p$ spaces. Using Zvonkin's transformation and estimates for solutions to Kolmogorov equations, we prove…

We establish the global existence of weak solutions to a nonlinear kinetic Fokker--Planck equation with degenerate diffusion, under either inflow or partial absorption-reflection boundary conditions. The novelty of our approach lies in…

We consider a class of models for nonlinearly elastic surfaces in this work. We have in mind thin, highly deformable structures modeled directly as two-dimensional nonlinearly elastic continua, accounting for finite membrane and bending…

Consider the following McKean-Vlasov SDE: $$ d X_t=\sqrt{2}d W_t+\int_{{\mathbb R}^d}K(t,X_t-y)\mu_{X_t}(dy)d t,\ \ X_0=x, $$ where $\mu_{X_t}$ stands for the distribution of $X_t$ and $K(t,x): {\mathbb R}_+\times{\mathbb R}^d\to{\mathbb…