Global Sobolev inequalities and degenerate p-Laplacian equations
نویسندگان
چکیده
منابع مشابه
Weighted Sobolev Spaces and Degenerate Elliptic Equations
In the case ω = 1, this space is denoted W (Ω). Sobolev spaces without weights occur as spaces of solutions for elliptic and parabolic partial differential equations. In various applications, we can meet boundary value problems for elliptic equations whose ellipticity is “disturbed” in the sense that some degeneration or singularity appears. This “bad” behaviour can be caused by the coefficient...
متن کاملNonlinear diffusions and optimal constants in Sobolev type inequalities: asymptotic behaviour of equations involving the p-Laplacian
We study the asymptotic behaviour of nonnegative solutions to: ut = pum using an entropy estimate based on a sub-family of the Gagliardo-Nirenberg inequalities – or, in the limit casem = (p 1) 1, on a logarithmic Sobolev inequality inW 1;p – for which optimal functions are known. Diffusions nonlinéaires et constantes optimales dans des inégalités de type Sobolev : comportement asymptotique d’éq...
متن کاملp-Laplacian problems with critical Sobolev exponent
We use variational methods to study the asymptotic behavior of solutions of p-Laplacian problems with nearly subcritical nonlinearity in general, possibly non-smooth, bounded domains.
متن کاملDegenerate P-laplacian Operators on H-type Groups and Applications to Hardy Type Inequalities
Abstract. Let G be a step-two nilpotent group of H-type with Lie algebra G = V ⊕ t. We define a class of vector fields X = {Xj} on G depending on a real parameter k ≥ 1, and we consider the corresponding p-Laplacian operator Lp,ku = divX(|∇Xu| ∇Xu). For k = 1 the vector fields X = {Xj} are the left invariant vector fields corresponding to an orthonormal basis of V , for k = 2 and G being the He...
متن کاملThe Solvability of Concave-Convex Quasilinear Elliptic Systems Involving $p$-Laplacian and Critical Sobolev Exponent
In this work, we study the existence of non-trivial multiple solutions for a class of quasilinear elliptic systems equipped with concave-convex nonlinearities and critical growth terms in bounded domains. By using the variational method, especially Nehari manifold and Palais-Smale condition, we prove the existence and multiplicity results of positive solutions.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2020
ISSN: 0022-0396
DOI: 10.1016/j.jde.2019.11.034