Singular limits of anisotropic Ginzburg-Landau functionalSpringer Science and Business Media LLC - - 2020
Xing-Bin Pan
We derive the asymptotic behavior of the minimizers of the anisotropic Ginzburg-Landau functional of superconductivity, as the ratio between the largest and smallest effective masses is very big, hence the effective mass tensor becomes very degenerate.
Symmetric-Convex Functionals of Linear GrowthSpringer Science and Business Media LLC - Tập 2 - Trang 59-71 - 2017
Franz Gmeineder
We discuss existence and regularity theorems for convex functionals of linear growth that depend on the symmetric rather than the full gradients. Due to the failure Korn’s Inequality in the L1-setup, the full weak gradients of minima do not need to exist, and the paper aims for presenting methods that help to overcome these issues as to partial regularity and higher integrability of minimisers.
Liouville theorems for superlinear parabolic problems with gradient structureSpringer Science and Business Media LLC - Tập 6 - Trang 145-153 - 2020
Pavol Quittner
We improve one of the methods for obtaining Liouville theorems for superlinear parabolic problems. In particular, if we consider a positively homogeneous gradient nonlinearity $$F:{{\mathbb {R}}}^m\rightarrow {{\mathbb {R}}}^m$$ of degree $$p>1$$, where $$n>2$$, $$p... hiện toàn bộ
Nonlinear scalar field equations with Berestycki–Lions’ nonlinearity on large domainsSpringer Science and Business Media LLC - Tập 6 - Trang 711-731 - 2020
Yohei Sato, Masataka Shibata
We prove the existence of solutions for the following semilinear elliptic equation:
$$\begin{aligned} - \Delta u = g(u) \quad \text {in } \Omega , \quad u \in H^1_0(\Omega ). \end{aligned}$$
Here
$$\Omega $$
is a suitable large domain and g satisfies the completely same conditions as Berestycki–Lions’ conditions. Those conditions of g are known as “almost sufficient and necessary conditions” ...... hiện toàn bộ
A Moser–Trudinger type inequality on the Orlicz fractional spaceSpringer Science and Business Media LLC - Tập 9 - Trang 33-62 - 2022
Abderrahmane Lakhdari, Nedra Belhaj Rhouma, Mounir Hsini
We prove the existence of a weak solution to the perturbed fractional Kirchhoff problem with a singular exponential nonlinearity that includes the fractional
$$\varphi$$
-laplacian operator. Our main results are obtained using Ekeland’s variational principle and the mountain pass theorem. To this e...... hiện toàn bộ