Related papers: A solution to the problem of $L^p-$maximal regular…

In this paper, we show mathematical justification of the data assimilation of nudging type in $L^p$-$L^q$ maximal regularity settings. We prove that the approximate solution of the primitive equations by data assimilation converges to the…

In this paper we show the weak Banach-Saks property of the Banach vector space $(L_\mu^p)^m$ generated by $m$ $L_\mu^p$-spaces for $1\leq p<+\infty,$ where $m$ is any given natural number. When $m=1,$ this is the famous Banach-Saks-Szlenk…

We prove regularity estimates for weak solutions to the Dirichlet problem for a divergence form elliptic operator. We give $L^p$ estimates for the second derivative for $p<2$. Our work generalizes results due to Miranda [28].

Here we utilize operator--valued Lq-Lp Fourier multiplier theorems to establish lower bound estimates for large class of elliptic integro-differential equations in Rd. Moreover, we investigate separability properties of parabolic…

Let $1\le p\le q<\infty$ and let $X$ be a $p$-convex Banach function space over a $\sigma$-finite measure $\mu$. We combine the structure of the spaces $L^p(\mu)$ and $L^q(\xi)$ for constructing the new space $S_{X_p}^{\,q}(\xi)$, where…

This paper revisits the H\"{o}lder regularity of mild solutions of parabolic stochastic Cauchy problems in Lebesgue spaces $L^p(\mathcal{O}),$ with $p\geq 2$ and $\mathcal{O}\subset\mathbb{R}^d$ a bounded domain. We find conditions on $p,…

In this paper, we introduce the so-called $L_p$ $q$-torsional measure for $p\in\mathbb{R}$ and $q>1$ by establishing the $L_p$ variational formula for the $q$-torsional rigidity of convex bodies without smoothness conditions. Moreover, we…

This paper is devoted to the study of $L_p$ Lyapunov-type inequalities for linear systems of equations with Neumann boundary conditions and for any constant $p \geq 1$. We consider ordinary and elliptic problems. The results obtained in the…

We study regularity issues and the limiting behavior as $p\to\infty$ of nonnegative solutions for elliptic equations of $p-$Laplacian type ($2 \leq p< \infty$) with a strong absorption: $$ -\Delta_p u(x) + \lambda_0(x) u_{+}^q(x) = 0 \quad…

It has been well known that if $\Omega$ is a bounded $C^1$-domain in $\R^n,\ n \ge 2$, then for every Radon measure $f$ on $\Omega$ with finite total variation, there exists a unique weak solution $u\in W_0^{1,1}(\Omega )$ of the Poisson…

We study the porous medium equation on manifolds with conical singularities. Given strictly positive initial values, we show that the solution exists in the maximal $L^{q}$-regularity space for all times and is instantaneously smooth in…

Let $(\Omega,\Sigma,\mu)$ be a measure space and $1< p < +\infty$. In this paper we show that, under quite general conditions, the set $L_{p}(\Omega) - \bigcup\limits_{1 \leq q < p}L_{q}(\Omega)$ is maximal spaceable, that is, it contains…

We establish the existence of a positive bounded weak solution for a class of Kirchhoff-type $p(\cdot)$-Laplacian problems involving an arbitrary growth and a sandwich-type growth $s(\cdot)\in (\inf p,\sup p)$. This setting leads to…

We study Banach spaces X with a strongly asymptotic l_p basis (any disjointly supported finite set of vectors far enough out with respect to the basis behaves like l_p) which are minimal (X embeds into every infinite dimensional subspace).…

In this paper, we prove the existence and uniqueness of nonnegative renormalized solutions for the fractional p(x)-Laplacian problem with L1 data. Our results are new even in the constant exponent fractional p-Laplacian equation case.

We prove a fixed point theorem for a family of Banach spaces, notably L^1 and its non-commutative analogues. Several applications are given, e.g. the optimal solution to the "derivation problem" studied since the 1960s.

Boundary value problem for complete second order elliptic equation is considered in Banach space. The equation and boundary conditions involve a small and spectral parameter. The uniform L_{p}-regularity properties with respect to space…

We start presenting an $L^{\infty}$-gradient bound for solutions to non-homogeneous $p$-Laplacean type systems and equations, via suitable non-linear potentials of the right hand side. Such a bound implies a Lorentz space characterization…

In this paper we study optimal control problems with either fractional or regional fractional $p$-Laplace equation, of order $s$ and $p\in [2,\infty)$, as constraints over a bounded open set with Lipschitz continuous boundary. The control,…

We consider stable solutions of semilinear elliptic equations of the form $-\Delta u=f(u)$ in a bounded domain $\Omega\subset\mathbb{R}^N$. In a well-known paper \cite{cfrs}, Cabr\'e, Figalli, Ros-Oton and Serra obtained interior estimates…