Related papers: Strongly nonlinear Robin problems for harmonic and…

We study a general nonlinear parabolic equation on a Lipschitz bounded domain in $\mathbb{R}^N$, \begin{equation*} \left\{\begin{array}{l l} \partial_t u-\mathrm{div} A(t,x,\nabla u)= f(t,x)&\text{in}\ \ \Omega_T,\\ u(t,x)=0 &\ \mathrm{ on}…

We consider a slightly subcritical Dirichlet problem with a non-power nonlinearity in a bounded smooth domain. For this problem, standard compact embeddings cannot be used to guarantee the existence of solutions as in the case of power-type…

We consider a non-autonomous Cauchy problem involving linear operators associated with time-dependent forms $a(t;.,.):V\times V\to {\mathbb{C}}$ where $V$ and $H$ are Hilbert spaces such that $V$ is continuously embedded in $H$. We prove…

We consider the behaviour of holomorphic functions on a bounded open subset of the plane, satisfying a Lipschitz condition with exponent $\alpha$, with $0<\alpha<1$, in the vicinity of an exceptional boundary point where all such functions…

This paper extends the Concentration-Compactness Principle to Musielak-Orlicz spaces, working in both bounded and unbounded domains. We show that our results include important special cases like classical Orlicz spaces, variable exponent…

We consider elliptic problems with nonclassical boundary conditions that contain additional unknown functions on the border of the domain of the elliptic equation and also contain boundary operators of higher orders with respect to the…

This paper investigates the asymptotic behavior of a class of nonlinear variational problems with Robin-type boundary conditions on a bounded Lipschitz domain. The energy functional contains a bulk term (the $p$-norm of the gradient), a…

In this paper we are concerned with the initial boundary value problems of linear and semi-linear parabolic equations with mixed boundary conditions on non-cylindrical domains in spatial-temporal space. We obtain the existence of a weak…

We investigate the measure of nodal sets for Robin and Neumann eigenfunctions in the domain and on the boundary of the domain. A polynomial upper bound for the interior nodal sets is obtained for Robin eigenfunctions in the smooth domain.…

The $\bar{\partial}$-Neumann problem is the fundamental boundary value problem in several complex variables. It features an elliptic operator coupled with non-coercive boundary conditions. The problem is globally regular on many, but not…

We completely characterize all nonlinear partial differential equations leaving a given finite-dimensional vector space of analytic functions invariant. Existence of an invariant subspace leads to a re duction of the associated dynamical…

Most of lipschitz regularity results for nonlinear strictly elliptic equations are obtained for a suitable growth power of the nonlinearity with respect to the gradient variable (subquadratic for instance). For equations with superquadratic…

We investigate the properties of certain elliptic systems leading, a~priori, to solutions that belong to the space of Radon measures. We show that if the problem is equipped with a so-called asymptotic Uhlenbeck structure, then the solution…

We study inverse boundary problems for semilinear Schr\"odinger equations on smooth compact Riemannian manifolds of dimensions $\ge 2$ with smooth boundary, at a large fixed frequency. We show that certain classes of cubic nonlinearities…

In this paper, for general $n\geq2$, we classify solutions to $n$-Laplacian Liouville equation with positive nonlinear Neumann boundary condition on the half-space $\mathbb{R}^{n}_{+}$. Under the positive nonlinear Neumann boundary…

Olver and Rosenau studied group-invariant solutions of (generally nonlinear) partial differential equations through the imposition of a side condition. We apply a similar idea to the special case of finite-dimensional Hamiltonian systems,…

We establish some existence and regularity results to the Dirichlet problem, for a class of quasilinear elliptic equations involving a partial differential operator, depending on the gradient of the solution. Our results are formulated in…

We consider a time-fractional parabolic equation of doubly nonlinear type, featuring nonlinear terms both inside and outside the differential operator in time. The main nonlinearities are maximal monotone graphs, without restrictions on the…

In this paper, the existence of smooth positive solutions to a Robin boundary-value problem with non-homogeneous differential operator and reaction given by a nonlinear convection term plus a singular one is established. Proofs chiefly…

We study the modular Hamiltonian of an interval for the ground state of a massive free scalar field on the half line with Robin boundary conditions, by employing a numerical method. When the interval is adjacent to the boundary, we find…