Search results for "p-Laplacian"

C1,α-regularity for variational problems in the Heisenberg group

2017

We study the regularity of minima of scalar variational integrals of $p$-growth, $1<p<\infty$, in the Heisenberg group and prove the H\"older continuity of horizontal gradient of minima.

Regularity properties of tug-of-war games and normalized equations

2017

Variational versus pseudomonotone operator approach in parameter-dependent nonlinear elliptic problems

2013

We study the existence of nontrivial solutions of parameter-dependent quasilinear elliptic Dirichlet problems of the form $-\Delta u = \lambda f(u)$ in $\Omega$, $u = 0$ on $\partial\Omega$, in a bounded domain $\Omega$ with sufficiently smooth boundary, where $\lambda$ is a real parameter and $\Delta_p$ denotes the p-Laplacian. Recently the authors obtained multiplicity results by employing an abstract localization principle of critical points of functional of the form $\Phi-\lambda\Psi$ on open subleveis of $\Phi$, i.e., of sets of the form $\Phi^{-1}(-\infty,r)$, combined with differential inequality techniques and topological arguments. Unlike in those recent papers by the authors, the …

Gradient nonlinear elliptic systems driven by a (p,q)-laplacian operator

2017

In this paper, using variational methods and critical point theorems, we prove the existence of multiple weak solutions for a gradient nonlinear Dirichlet elliptic system driven by a (p, q)-Laplacian operator.

Equivalence of viscosity and weak solutions for a $p$-parabolic equation

2019

AbstractWe study the relationship of viscosity and weak solutions to the equation $$\begin{aligned} \smash {\partial _{t}u-\varDelta _{p}u=f(Du)}, \end{aligned}$$ ∂ t u - Δ p u = f ( D u ) , where $$p&gt;1$$ p &gt; 1 and $$f\in C({\mathbb {R}}^{N})$$ f ∈ C ( R N ) satisfies suitable assumptions. Our main result is that bounded viscosity supersolutions coincide with bounded lower semicontinuous weak supersolutions. Moreover, we prove the lower semicontinuity of weak supersolutions when $$p\ge 2$$ p ≥ 2 .

Hölder regularity for the gradient of the inhomogeneous parabolic normalized p-Laplacian

2018

In this paper, we study an evolution equation involving the normalized [Formula: see text]-Laplacian and a bounded continuous source term. The normalized [Formula: see text]-Laplacian is in non-divergence form and arises for example from stochastic tug-of-war games with noise. We prove local [Formula: see text] regularity for the spatial gradient of the viscosity solutions. The proof is based on an improvement of flatness and proceeds by iteration.

Remarks on regularity for p-Laplacian type equations in non-divergence form

2018

We study a singular or degenerate equation in non-divergence form modeled by the $p$-Laplacian, $$-|Du|^\gamma\left(\Delta u+(p-2)\Delta_\infty^N u\right)=f\ \ \ \ \text{in}\ \ \ \Omega.$$ We investigate local $C^{1,\alpha}$ regularity of viscosity solutions in the full range $\gamma>-1$ and $p>1$, and provide local $W^{2,2}$ estimates in the restricted cases where $p$ is close to 2 and $\gamma$ is close to 0.