Related papers: The $L_q$ Minkowski problem for $\mathbf{p}$-harmo…
We establish an explicit $L^\infty(\Om)$ a priori estimate for weak solutions to subcritical elliptic problems with nonlinearity on the boundary, in terms of the powers of their $H^1(\Om)$ norms. To prove our result, we combine in a novel…
The $L_{p}$ Gaussian Minkowski problem for $C$-pseudo-cones is studied in this paper, and the existence and uniqueness results are established. This extends our previous work on the Minkowski problem for $C$-pseudo-cones with respect to the…
Let $A_1$ and $A_2$ be two circular annuli and let $\rho$ be a radial metric defined in the annuli $A_2$. We study the existence and uniqueness of the extremal problem for weighted combined energy between $A_1$ and $A_2$, and obtain that…
A short account of recent existence and multiplicity theorems on the Dirichlet problem for an elliptic equation with $(p,q)$-Laplacian in a bounded domain is performed. Both eigenvalue problems and different types of perturbation terms are…
The aim of the paper is to prove the existence and uniqueness of the $L^{p}$--variational solution, with $p>1,$ of the following multivalued backward stochastic differential equation with $p$--integrable data: \begin{equation*} \left\{…
We construct N-harmonic functions in a domain with one isolated singularity on the boundary of the domain. By using solutions of the spherical p-harmonic spectral problem, we give an inductive method to produce a large variety of separable…
We introduce a new notion of a harmonic measure for a $d$-dimensional set in $\R^n$ with $d<n-1$, that is, when the codimension is strictly bigger than 1. Our measure is associated to a degenerate elliptic PDE, it gives rise to a…
In this paper, we first obtain an $L^q$ gradient estimate for $p$-harmonic maps, by assuming the target manifold supporting a certain function, whose gradient and Hessian satisfy some analysis conditions. From this $L^q$ gradient estimate,…
This paper studies a maximal $L^q$-regularity property for nonlinear elliptic equations of second order with a zero-th order term and gradient nonlinearities having superlinear and sub-quadratic growth, complemented with Dirichlet boundary…
We consider the Dirichlet problem Lu = 0 in D u = g on E = boundary of D for two second order elliptic operators L_k(u) = \sum_{i,j=1}^n a_k^{ij}(x) \partial_{ij} u(x), k=0,1, in a bounded Lipschitz domain D in R^n. The coefficients…
Given two elliptic operators L and M in nondivergence form, with coefficients A_L(x), A_M(x) and drift terms b_L(x), b_M(x), respectively, satisfying a Carleson measure disagreement condition in a Lipschitz domain Omega in R^{n+1}, then…
A numerical framework to explore the Brill Wave Initial Value Problem is presented along with a review of some of the theoretical predictions concerning Brill waves. It is demonstrated that there is an agreement between the numerically…
In this note we study the $L^p-L^q$ boundedness of Fourier multipliers of anharmonic oscillators, and as a consequence also of spectral multipliers, for the range $1<p \leq 2 \leq q <\infty$. The underlying Fourier analysis is associated…
We provide a general approach to Lipschitz regularity of solutions for a large class of vector-valued, nonautonomous variational problems exhibiting nonuniform ellipticity. The functionals considered here range amongst those with unbalanced…
We discuss the smoothness and strict convexity of the solution of the $L_p$ Minkowski problem when $p<1$ and the given measure has a positive density function.
Within the setting of metric spaces equipped with a doubling measure and supporting a $p$-Poincar\'e inequality, establishing existence of solutions to Dirichlet problem in a bounded domain in such a metric space is accomplished via direct…
Comparison estimates are an important technical device in the study of regularity problems for quasilinear possibly degenerate elliptic and parabolic equations. Such tools have been employed indispensably in many papers of Mingione,…
In this paper, exploiting variational methods, the existence of multiple weak solutions for a class of elliptic Navier boundary problems involving the $p$-biharmonic operator is investigated. Moreover, a concrete example of an application…
In this paper, we prove a sharp anisotropic $L^p$ Minkowski inequality involving the total $L^p$ anisotropic mean curvature and the anisotropic $p$-capacity, for any bounded domains with smooth boundary in $\mathbb{R}^n$. As consequences,…
In this paper we prove the~existence of two non-trivial weak solutions of Dirichlet boundary value problem for p-Laplacian problem with a~singular part and two disturbances satisfying the~proper assumptions. The~abstract existence result we…