scholarly journals Hölder continuous solutions of Boussinesq equation with compact support

2017 ◽  
Vol 272 (10) ◽  
pp. 4334-4402 ◽  
Author(s):  
Tao Tao ◽  
Liqun Zhang
Keyword(s):  
Compact Support ◽  
Boussinesq Equation ◽  
Continuous Solutions ◽  
Hölder Continuous

Gluing Solutions

2017 ◽  
Author(s):  
Philip Isett
Keyword(s):  
Stress Tensor ◽  
Compact Support ◽  
Smooth Solution ◽  
Continuous Solution ◽  
Total Momentum ◽  
Frame Of Reference ◽  
Galilean Transformation ◽  
Hölder Continuous ◽  
Pressure Form ◽  
Original Frame

This chapter deals with the gluing of solutions and the relevant theorem (Theorem 12.1), which states the condition for a Hölder continuous solution to exist. By taking a Galilean transformation if necessary, the solution can be assumed to have zero total momentum. The cut off velocity and pressure form a smooth solution to the Euler-Reynolds equations with compact support when coupled to a smooth stress tensor. The proof of Theorem (12.1) proceeds by iterating Lemma (10.1) just as in the proof of Theorem (10.1). Applying another Galilean transformation to return to the original frame of reference, the theorem is obtained.

scholarly journals Continuous solutions to two iterative functional equations

2021 ◽  
Author(s):  
Karol Baron
Keyword(s):  
Probability Measure ◽  
Functional Equations ◽  
Continuous Functions ◽  
Continuous Solutions ◽  
Hölder Continuous ◽  
Hölder Continuous Functions

AbstractBased on iteration of random-valued functions we study the problem of solvability in the class of continuous and Hölder continuous functions $$\varphi $$ φ of the equations $$\begin{aligned} \varphi (x)=F(x)-\int _{\Omega }\varphi \big (f(x,\omega )\big )P(d\omega ),\\ \varphi (x)=F(x)+\int _{\Omega }\varphi \big (f(x,\omega )\big )P(d\omega ), \end{aligned}$$ φ ( x ) = F ( x ) - ∫ Ω φ ( f ( x , ω ) ) P ( d ω ) , φ ( x ) = F ( x ) + ∫ Ω φ ( f ( x , ω ) ) P ( d ω ) , where P is a probability measure on a $$\sigma $$ σ -algebra of subsets of $$\Omega $$ Ω .

Existence and Hölder continuity to solutions of the complex Monge–Ampère-type equations with measures vanishing on pluripolar subsets

2021 ◽  
Author(s):  
Le Mau Hai ◽  
Vu Van Quan
Keyword(s):  
Pseudoconvex Domain ◽  
Hölder Continuity ◽  
Type Equation ◽  
Holder Continuity ◽  
Continuous Solutions ◽  
Hölder Continuous ◽  
Strictly Pseudoconvex Domain ◽  
Monge Ampere

In this paper, we establish existence of Hölder continuous solutions to the complex Monge–Ampère-type equation with measures vanishing on pluripolar subsets of a bounded strictly pseudoconvex domain [Formula: see text] in [Formula: see text].

scholarly journals Hölder continuous solutions to Monge–Ampère equations

2014 ◽  
Vol 16 (4) ◽  
pp. 619-647 ◽  
Author(s):  
Jean-Pierre Demailly ◽  
Sławomir Dinew ◽  
Vincent Guedj ◽  
Pham Hoang Hiep ◽  
Sławomir Kołodziej ◽  
...  
Keyword(s):  
Continuous Solutions ◽  
Hölder Continuous ◽  
Monge Ampere

scholarly journals Hölder continuous solutions to Monge-Ampère equations

2008 ◽  
Vol 40 (6) ◽  
pp. 1070-1080 ◽  
Author(s):  
V. Guedj ◽  
S. Kolodziej ◽  
A. Zeriahi
Keyword(s):  
Continuous Solutions ◽  
Hölder Continuous ◽  
Monge Ampere

scholarly journals Regularity of Hölder continuous solutions of the supercritical porous media equation

2013 ◽  
Vol 2013 (1) ◽  
Author(s):  
Wenxin Yu ◽  
Yigang He ◽  
Yaonan Tong ◽  
Qiwu Luo ◽  
Xianming Wu
Keyword(s):  
Porous Media ◽  
Porous Media Equation ◽  
Continuous Solutions ◽  
Hölder Continuous ◽  
Media Equation
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