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We prove existence, uniqueness and regularity results for mixed boundary value problems associated with fully nonlinear, possibly singular or degenerate elliptic equations. Our main result is a global H\"older estimate for solutions,…
We consider a rigid body freely moving in a compressible inviscid fluid within a bounded domain $\Omega\subset\mathbb{R}^3$. The fluid is thereby governed by the non necessarily isentropic compressible Euler equations, while the rigid body…
Motivated by an analysis on the well-posedness of the initial boundary value problem for the motion of an inextensible hanging string, we first consider an initial boundary value problem for one-dimensional degenerate hyperbolic systems…
We study small perturbations of the Dirichlet problems for second order elliptic equations that degenerate on the boundary. The limit of the solution, as the perturbation tends to zero, is calculated. The result is based on a certain…
In this paper we establish weighted $L^{q}$-$L^{p}$-maximal regularity for linear vector-valued parabolic initial-boundary value problems with inhomogeneous boundary conditions of static type. The weights we consider are power weights in…
Motivated by a new kind of initial boundary value problem (IBVP) with a free boundary arising in wave-structure interaction, we propose here a general approach to one-dimensional IBVP as well as transmission problems. For general strictly…
In this paper, we study the local exact boundary controllability of entropy solutions to a class linearly degenerate hyperbolic systems of conservation laws with constant multiplicity. The authors prove the two-sided boundary…
We prove the well-posedness and regularity of solutions in mixed-norm weighted Sobolev spaces for a class of second-order parabolic and elliptic systems in divergence form in the half-space $\mathbb{R}^d_+ = \{x_d > 0\}$ subject to the…
In this paper we study the quasilinear nondiagonal parabolic type systems. We assume that the principal elliptic operator, which is part of the parabolic system, has a divergence structure. Under certain conditions it is proved the…
The Virasoro minimal models with boundary are described in the Landau-Ginzburg theory by introducing a boundary potential, function of the boundary field value. The ground state field configurations become non-trivial and are found to obey…
We study fully nonlinear singularly perturbed parabolic equations and their limits. We show that solutions are uniformly Lipschitz continuous in space and H\"{o}lder continuous in time. For the limiting free boundary problem, we analyse the…
We study the problem of inviscid slightly compressible fluids in a bounded domain. We find a unique solution to the initial-boundary value problem and show that it is near the analogous solution for an incompressible fluid provided the…
This work is concerned with the possibility of proving the boundary null controllability for the degenerate wave equation, developing the asymptotic analysis of a suitable family of state-control pairs $((u_\varepsilon ,…
In this paper there are estimated the derivatives of the solution of an initial boundary value problem for a nonlinear uniformly parabolic equation in the interior with the total variation of the boundary data and the L^{infinity}-norm of…
We consider a parabolic non-local free boundary problem that has been derived as a limit of a bulk-surface reaction-diffusion system which models cell polarization. The authors have justified the well-posedness of this problem and have…
The probabilistic representation of weak solutions to a parabolic boundary value problem is established in the following framework. The boundary value problem consists of a second order parabolic equation defined on a time-varying Lipschitz…
In this paper we outline a general method for finding well-posed boundary value problems for linear equations of mixed elliptic and hyperbolic type, which extends previous techniques of Berezanskii, Didenko, and Friedrichs. This method is…
We consider equations of the form $\Delta u +\lambda^2 V(x)e^{\,u}=\rho$ in various two dimensional settings. We assume that $V>0$ is a given function, $\lambda>0$ is a small parameter and $\rho=\mathcal O(1)$ or $\rho\to +\infty$ as…
We consider boundary value problems for quasilinear first-order one-dimensional hyperbolic systems in a strip. The boundary conditions are supposed to be of a smoothing type, in the sense that the $L^2$-generalized solutions to the…
We study a class of degenerate parabolic equations with boundary point degeneracy in dimensions N>=2 and investigate the associated boundary observability problem by means of shape design. While one-dimensional degenerate models have been…