Related papers: Energy quantization and mean value inequalities fo…

We prove nonlinear lower bounds and commutator estimates for the Dirichlet fractional Laplacian in bounded domains. The applications include bounds for linear drift-diffusion equations with nonlocal dissipation and global existence of weak…

We show existence of solutions for the equations of static atomistic nonlinear elasticity theory on a bounded domain with prescribed boundary values. We also show their convergence to the solutions of continuum nonlinear elasticity theory,…

We consider boundary value problems of the first and third kind for the diffusionwave equation. By using the method of energy inequalities, we find a priori estimates for the solutions of these boundary value problems.

We study a quite general family of nonlinear evolution equations of diffusive type with nonlocal effects. More precisely, we study porous medium equations with a fractional Laplacian pressure, and the problem is posed on a bounded space…

We generalize the well-known mean value inequality of subharmonic functions for a slightly more general function class. We also apply this generalized mean value inequality to weighted boundary behavior and nonintegrability questions of…

For differential inequalities with the $\infty$-Laplacian in the principal part, we obtain conditions for the absence of solutions in unbounded domains. Examples are given to demonstrate the accuracy of these conditions.

We deal with critical nonlinear problems involving the p-Laplacian operator on bounded domains with mixed boundary conditions. We prove the existence of least energy solutions. Our work shows a significant difference between the semi-linear…

This paper provides a quantitative study of nonnegative solutions to nonlinear diffusion equations of porous medium-type of the form $\partial_t u + {\mathcal L}u^m=0$, $m>1$, where the operator ${\mathcal L}$ belongs to a general class of…

We consider an aggregation model with nonlinear diffusion in domains with boundaries and investigate the zero diffusion limit of its solutions. We establish the convergence of weak solutions for fixed times, as well as the convergence of…

We derive a class of energy preserving boundary conditions for incompressible Newtonian flows and prove local-in-time well-posedness of the resulting initial boundary value problems, i.e. the Navier-Stokes equations complemented by one of…

We construct viscosity solutions to the nonlinear evolution equation \eqref{p} below which generalizes the motion of level sets by mean curvature (the latter corresponds to the case $p = 1$) using the regularization scheme as in \cite{ES1}…

We consider a boundary value problem for the system of equations describing the stationary motion of a viscous nonhomogeneous asymmetric fluid in a bounded planar domain having a $C^2$ boundary. We use a stream-function formulation after…

We consider a quasi-linear parabolic equation with nonlinear dynamic boundary conditions occurring as a natural generalization of the semilinear reaction-diffusion equation with dynamic boundary conditions. The corresponding class of…

We study a Dirichlet boundary problem related to the fractional Laplacian in a manifold. Its variational formulation arises in the study of magnitude, an invariant of compact metric spaces given by the reciprocal of the ground state energy.…

We introduce a new Neumann problem for the fractional Laplacian arising from a simple probabilistic consideration, and we discuss the basic properties of this model. We can consider both elliptic and parabolic equations in any domain. In…

We consider a number of boundary value problems involving the $p$-Laplacian. The model case is $-\Delta_p u=V|u|^{p-2}u$ for $u\in W_0^{1,2}(D)$ with $D$ a bounded domain in ${\bf R}^n$. We derive necessary conditions for the existence of…

We study the quantitative unique continuation on the boundary for solutions of elliptic equations with Neumann boundary conditions for bounded potentials and boundary potentials on compact manifolds with boundary. The boundary doubling…

We study the rate of convergence for (variational) eigenvalues of several non-linear problems involving oscillating weights and subject to different kinds of boundary conditions in bounded domains.

In this paper we deal with the following boundary value problem \begin{equation*} \begin{cases} -\Delta_{p}u + g(u) | \nabla u|^{p} = h(u)f & \text{in $\Omega$,} \newline u\geq 0 & \text{in $\Omega$,} \newline u=0 & \text{on $\partial…

We develop a notion of quantum observable for the general boundary formulation of quantum theory. This notion is adapted to spacetime regions rather than to hypersurfaces and naturally fits into the topological quantum field theory like…