A degenerate fully nonlinear free transmission problem with variable exponents

AbstractWe investigate strong maximum (and minimum) principles for fully nonlinear second-order equations on Riemannian manifolds that are non-totally degenerate and satisfy appropriate scaling conditions. Our results apply to a large class of nonlinear operators, among which Pucci’s extremal operators, some singular operators such as those modeled on the p- and $$\infty $$ ∞ -Laplacian, and mean curvature-type problems. As a byproduct, we establish new strong comparison principles for some second-order uniformly elliptic problems when the manifold has nonnegative sectional curvature.

Download Full-text

Stability Results of an Elastic/Viscoelastic Transmission Problem of Locally Coupled Waves with Non Smooth Coefficients

Acta Applicandae Mathematicae ◽

10.1007/s10440-021-00384-8 ◽

2021 ◽

Vol 171 (1) ◽

Author(s):

Ali Wehbe ◽

Ibtissam Issa ◽

Mohammad Akil

Keyword(s):

Transmission Problem ◽

Smooth Coefficients ◽

Stability Results

Download Full-text

Positive solutions of a discrete second-order boundary value problems with fully nonlinear term

Advances in Difference Equations ◽

10.1186/s13662-020-03039-4 ◽

2020 ◽

Vol 2020 (1) ◽

Author(s):

Liyun Jin ◽

Hua Luo

Keyword(s):

Positive Solutions ◽

Fixed Point Index ◽

Nonlinear Term ◽

Boundary Value ◽

Index Theory ◽

Second Order ◽

Fully Nonlinear ◽

Fixed Point Index Theory ◽

Weaker Conditions ◽

Lower Limits

Abstract In this paper, we mainly consider a kind of discrete second-order boundary value problem with fully nonlinear term. By using the fixed-point index theory, we obtain some existence results of positive solutions of this kind of problems. Instead of the upper and lower limits condition on f, we may only impose some weaker conditions on f.

Download Full-text

Existence of Solutions with Asymptotic Behavior of Exterior Problems of Fully Nonlinear Uniformly Elliptic Equations

2011 Fourth International Symposium on Knowledge Acquisition and Modeling ◽

10.1109/kam.2011.63 ◽

2011 ◽

Author(s):

Limei Da

Keyword(s):

Asymptotic Behavior ◽

Elliptic Equations ◽

Existence Of Solutions ◽

Fully Nonlinear ◽

Exterior Problems

Download Full-text

Variable Anisotropic Hardy Spaces with Variable Exponents

Analysis and Geometry in Metric Spaces ◽

10.1515/agms-2020-0124 ◽

2021 ◽

Vol 9 (1) ◽

pp. 65-89

Author(s):

Zhenzhen Yang ◽

Yajuan Yang ◽

Jiawei Sun ◽

Baode Li

Keyword(s):

Hardy Spaces ◽

Variable Exponent ◽

Atomic Decomposition ◽

Integral Operators ◽

Moment Condition ◽

Variable Exponents ◽

Hölder Continuous ◽

Multi Level ◽

The Moment ◽

Variable Anisotropy

Abstract Let p(·) : ℝ n → (0, ∞] be a variable exponent function satisfying the globally log-Hölder continuous and let Θ be a continuous multi-level ellipsoid cover of ℝ n introduced by Dekel et al. [12]. In this article, we introduce highly geometric Hardy spaces Hp (·)(Θ) via the radial grand maximal function and then obtain its atomic decomposition, which generalizes that of Hardy spaces Hp (Θ) on ℝ n with pointwise variable anisotropy of Dekel et al. [16] and variable anisotropic Hardy spaces of Liu et al. [24]. As an application, we establish the boundedness of variable anisotropic singular integral operators from Hp (·)(Θ) to Lp (·)(ℝ n ) in general and from Hp (·)(Θ) to itself under the moment condition, which generalizes the previous work of Bownik et al. [6] on Hp (Θ).

Download Full-text