We study unbounded weak supersolutions of elliptic partial differential equations with generalized Orlicz (Musielak--Orlicz) growth. show that they satisfy the Harnack inequality optimal exponent provided belong to a suitable Lebesgue or Sobolev space. Furthermore, we establish sharpness our central assumptions.

Statistics requires consideration of the “ideal estimates” defined through the posterior mean of fractional powers of finite measures. In this paper we study L1= , the linear space spanned by th power of finite measures, 2 (0; 1). It is shown that L1= generalizes the Lebesgue function space L1= ( ), and shares most of its important properties: It is a uniformly convex (hence reflexive) Banach s...

We prove the existence of at least three weak solutions for the Dirichlet problem when the nonlinear term f is sublinear and p(x) is greater than n. This Dirichlet problem involves a general elliptic operator in divergence form (in particular, a p(x)-Laplace operator). Our method relies upon a recent critical point theorem obtained by Bonanno and Marano, and is combined with the theory of varia...

The relationship between the operator norms of fractional integral operators acting on weighted Lebesgue spaces and the constant of the weights is investigated. Sharp bounds are obtained for both the fractional integral operators and the associated fractional maximal functions. As an application improved Sobolev inequalities are obtained. Some of the techniques used include a sharp off-diagonal...

In this paper, we study the Gibbs measures for periodic generalized Korteweg-de Vries equations (gKdV) with quartic or higher nonlinearities. order to bypass analytical ill-posedness of equation in Sobolev support measures, establish deterministic well-posedness gauged gKdV within framework Fourier-Lebesgue spaces. Our argument relies on bilinear and trilinear Strichartz estimates adapted setti...

<p style='text-indent:20px;'>We consider a general inhomogeneous parabolic initial-boundary value problem for <inline-formula><tex-math id="M1">\begin{document}$ 2b $\end{document}</tex-math></inline-formula>-parabolic differential equation given in finite multidimensional cylinder. We investigate the solvability of this some generalized anisotropic Sobolev spaces....

In this paper, we prove the existence and regularity of weak solutions for a class nonlinear elliptic equations with degenerate coercivity singular lower-order terms natural growth respect to gradient Lm(⋅) (m(x)≥1) data. The functional setting involves Lebesgue–Sobolev spaces variable exponents.

We present an existence theory based on minimization of the nonlocal energies appearing in peridynamics, which is a nonlocal continuum model in solid mechanics that avoids the use of deformation gradients. We employ the direct method of the calculus of variations in order to find minimizers of the energy of a deformation. Lower semicontinuity is proved under a weaker condition than convexity, w...