scholarly journals Hölder continuity of solutions to the complex Monge–Ampère equation with the right-hand side in L p : the case of compact Kähler manifolds

2008 ◽  
Vol 342 (2) ◽  
pp. 379-386 ◽  
Author(s):  
Sławomir Kołodziej
Keyword(s):  
Hölder Continuity ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Holder Continuity ◽  
Right Hand ◽  
Continuity Of Solutions ◽  
The Right ◽  
Monge Ampere

scholarly journals A remark on covering of compact Kähler manifolds and applications

2021 ◽  
Vol 73 (1) ◽  
pp. 138-148
Author(s):  
V. V. Hung ◽  
H. N. Quy
Keyword(s):  
Upper Bound ◽  
Kähler Manifold ◽  
Kahler Manifolds ◽  
Hölder Continuous ◽  
Kahler Manifold ◽  
Right Hand ◽  
Regularization Techniques ◽  
The Right ◽  
Compact Kähler Manifold ◽  
Monge Ampere

UDC 517.9 Recently, Kolodziej proved that, on a compact Kähler manifold the solutions to the complex Monge – Ampére equation with the right-hand side in are Hölder continuous with the exponent depending on and (see [Math. Ann., <strong>342</strong>, 379-386 (2008)]).Then, by the regularization techniques in[J. Algebraic Geom., <strong>1</strong>, 361-409 (1992)], the authors in [J. Eur. Math. Soc., <strong>16</strong>, 619-647 (2014)] have found the optimal exponent of the solutions.In this paper, we construct a cover of the compact Kähler manifold which only depends on curvature of Then, as an application, base on the arguments in[Math. Ann., <strong>342</strong>, 379-386 (2008)], we show that the solutions are Hölder continuous with the exponent just depending on the function in the right-hand side and upper bound of curvature of  

Hölder continuous potentials on manifolds with partially positive curvature

2010 ◽  
Vol 9 (4) ◽  
pp. 705-718 ◽  
Author(s):  
Sławomir Dinew
Keyword(s):  
Positive Curvature ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Hölder Continuous ◽  
Bisectional Curvature ◽  
Right Hand ◽  
Monge Ampere

AbstractIt is proved that solutions of the complex Monge–Ampère equation on compact Kähler manifolds with right hand side in Lp, p > 1, are uniformly Hölder continuous under the assumption on non-negative orthogonal bisectional curvature.

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].

On the continuity of solutions of the equations of a porous medium and the fast diffusion with weighted and singular lower-order terms

2021 ◽  
Vol 18 (1) ◽  
pp. 104-139
Author(s):  
Yevhen Zozulia
Keyword(s):  
Porous Medium ◽  
Parabolic Equation ◽  
Harnack Inequality ◽  
Lower Order ◽  
Riesz Potential ◽  
Fast Diffusion ◽  
Right Hand ◽  
Continuity Of Solutions ◽  
The Right ◽  
Lower Order Terms

For the parabolic equation $$ \ v\left(x \right)u_{t} -{div({\omega(x)u^{m-1}}} \nabla u) = f(x,t)\: ,\; u\geq{0}\:,\; m\neq{1} $$ we prove the continuity and the Harnack inequality for generalized k solutions, by using the weighted Riesz potential on the right-hand side of the equation.

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