Existence of entropy solutions for nonlinear elliptic degenerate anisotropic equations
Open Mathematics, 2017 In the present article we deal with the Dirichlet problem for a class of degenerate anisotropic elliptic second-order equations with L1-right-hand sides in a bounded domain of ℝn(n ⩾ 2) . This class is described by the presence of a set of exponents q1,…,
Gorban Yuliya
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Besov regularity for the elliptic p-harmonic equations in the non-quadratic case
Advances in Nonlinear AnalysisIn this article, we mainly establish the local extra fractional differentiability (Besov regularity) of weak solutions for the following divergence nonlinear elliptic equations of pp-Laplacian type: divA(Du,x)=divF,\hspace{0.1em}\text{div}\hspace{0.1em}A(
Yao Fengping
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Rigidity results for some boundary quasilinear phase transitions
, 2008 We consider a quasilinear equation given in the half-space, i.e. a so called boundary reaction problem. Our concerns are a geometric Poincar\'e inequality and, as a byproduct of this inequality, a result on the symmetry of low-dimensional bounded stable ...
Sire, Yannick, Valdinoci, Enrico
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Existence for (p, q) critical systems in the Heisenberg group
Advances in Nonlinear Analysis, 2019 This paper deals with the existence of entire nontrivial solutions for critical quasilinear systems (𝓢) in the Heisenberg group ℍn, driven by general (p, q) elliptic operators of Marcellini types.
Pucci Patrizia, Temperini Letizia
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A Bernoulli problem with non constant gradient boundary constraint [PDF]
, 2010 We present in this paper a result about existence and convexity of solutions to a free boundary problem of Bernoulli type, with non constant gradient boundary constraint depending on the outer unit normal. In particular we prove that, in the convex case,
Bianchini, Chiara
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Regularity for double-phase functionals with nearly linear growth and two modulating coefficients
Advances in Nonlinear AnalysisWe deal with non-uniformly elliptic integral functionals w↦∫c(x)∣Dw∣log(1+∣Dw∣)+a(x)(∣Dw∣2+s2)q2+1dx,w\mapsto \int \left[{\mathfrak{c}}\left(x)| Dw| \log \left(1+| Dw| )+a\left(x){\left({| Dw| }^{2}+{s}^{2})}^{\tfrac{q}{2}}+1\right]{\rm{d}}x, with s∈[0,1]
Kim Bogi, Oh Jehan
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Existence and non-existence of solutions to a Hamiltonian strongly degenerate elliptic system
Advances in Nonlinear Analysis, 2017 We study the non-existence and existence of infinitely many solutions to the semilinear degenerate elliptic ...
Anh Cung The, My Bui Kim
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Bifurcation and multiplicity results for critical problems involving the p-Grushin operator
Advances in Nonlinear AnalysisIn this article, we prove a bifurcation and multiplicity result for a critical problem involving a degenerate nonlinear operator Δγp{\Delta }_{\gamma }^{p}. We extend to a generic p>1p\gt 1 a result, which was proved only when p=2p=2. When p≠2p\ne 2, the
Malanchini Paolo +2 more
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On a nonlinear Robin problem with an absorption term on the boundary and L1 data
Advances in Nonlinear AnalysisWe deal with existence and uniqueness of nonnegative solutions to: −Δu=f(x),inΩ,∂u∂ν+λ(x)u=g(x)uη,on∂Ω,\left\{\begin{array}{ll}-\Delta u=f\left(x),\hspace{1.0em}& \hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0.33em}\Omega ,\\ \frac{\partial u}{\partial ...
Pietra Francesco Della +2 more
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Global and blow up solutions to cross diffusion systems
Advances in Nonlinear Analysis, 2015 Necessary and sufficient conditions for global existence of classical solutions to a class of cross diffusion systems on n-dimensional domains are given. Examples of blow up solutions are also presented.
Ahmad Shair, Le Dung
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