Anisotropic and inhomogeneous spaces, which are at the core of the present study, may
appear exotic at first. However, the reader should abandon this impression once they realize …

Let $\Omega\subseteq\mathbb {R}^ N $ a bounded open set, $ N\geq 2$, and let $ p> 1$;
we prove existence of a renormalized solution for parabolic problems whose model is …

We consider the nonlinear heat equation (with Leray-Lions operators) on an open bounded
subset of RN with Dirichlet homogeneous boundary conditions. The initial condition is in L 1 …

Given a parabolic cylinder Q=(0, T)× Ω, where Ω ⊂ R^ N is a bounded domain, we prove
new properties of solutions of u_t-\Delta_p u= μ\quad in Q with Dirichlet boundary …

We consider a class of nonlinear elliptic equations containing a p-Laplacian type operator,
lower order terms having natural growth with respect to the gradient, and bounded …

We prove existence and uniqueness of renormalized solutions to general nonlinear
parabolic equation in Musielak–Orlicz space avoiding growth restrictions. Namely, we …

We will present the proof of existence of renormalized solutions to a nonlinear parabolic
problem∂ tu− div a (⋅, D u)= f with right-hand side f and initial data u 0 in L 1. The growth …

The paper is concerned with the optimal harvesting of a marine park, which is described by
a parabolic heat equation with Neumann boundary conditions and a nonlinear source term …

We propose a probabilistic definition of solutions of semilinear elliptic equations with
(possibly nonlocal) operators associated with regular Dirichlet forms and with measure data …

In this article we prove the existence and uniqueness of entropy solutions for p (x)-Laplace
equations with a Radon measure which is absolutely continuous with respect to the relative …