# On Beltrami equations and Holder regularity

On the regularity of solutions to the Beltrami equation in a plane

The author wish to thank Professor T. Iwaniec for letting her include in this paper Example 4. Maz'ya and R.

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### Submission history

As a consequence of 3. Saksman, "Beltrami operators in the plane," Duke Mathematical Journal, vol. Citation Only. Iwaniec, and C. Chen, Traveling wave solutions in parametric forms for a diffusion model with a nonlinear rate of growth ,, Discrete Contin. Iwaniec, The p-harmonic transform beyond its natural domain of definition ,, Indiana Univ. Parameterizing General Linear Elliptic Systems.

D'Onofrio, T. Iwaniec, and C.

Sbordone, "G-closed classes of elliptic operators in the complex plane," Ricerche di Matematica, vol. Astala and J. Fabes and D.

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Stroock, "The Lp-integrability of Green's functions and fundamental solutions for elliptic and parabolic equations," Duke Mathematical Journal, vol. D'Onofrio and L. Pucci, "Un problema variazionale per i coefficienti di equazioni differenziali di tipo ellittico," vol. Chiarenza, M. Frasca, and P. Longo, "Interior W2,p estimates for nondivergence elliptic equations with discontinuous coefficients," Ricerche di Matematica, vol. Kim and N. Iwaniec, and E.

Saksman, "Beltrami operators in the plane," Duke Mathematical Journal, vol. Talenti, "Equazioni lineari ellittiche in due variabili," Le Matematiche, vol. Gilbarg and N. However, users may print, download, or email articles for individual use. CC BY. Estimates for operators on weighted Morrey spaces and their applications to nondivergence elliptic equations. Optimal regular differential operators with variable coefficients and applications.

Sharp estimates for commutators of singular integrals via iterations of the Hardy-Littlewood maximal function. Definitions and Notations In order to describe the results of the present paper, it is necessary to introduce some definitions. The first example deals with adjoint solutions which are partial derivatives hXl and hx2 of a very weak solution h e Wlo'c to a particular diagonal divergence type equation, and an interesting relation comes out between regularity results.

We proceed similarly as in [6]. See [7, Theorem 3. Theorem 3.

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Then, one has Mk M. In order to prove Proposition 3. Br 0 fails.

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We estimate the Hoelder exponent $\alpha$ of solutions to the Beltrami equation $\dbar f=\mu\de f$, where the Beltrami coefficient satisfies $\|\mu\|_\infty<1$. Request PDF on ResearchGate | On planar Beltrami equations and Holder regularity | We provide estimates for the Holder exponent of solutions to the Beltrami.

Lin and L. Notes Math. Harlow , , Iwaniec and C. Sbordone, Weak minima of variational integrals ,, J. Reine Angew Math.

Koskela and O. Lindqvist and O. Martio, Two theorems of N.

## On the regularity of solutions to the Beltrami equation in a plane

Wiener for solutions of quasilinear elliptic equations ,, Acta Math. Ladyzhenskaya and N. Translation of Math Monographs , 73 Serrin and H. Zou, Cauchy-Liouville and universal boundedness theorems for quasilinear elliptic equations and inequalities ,, Acta Math. Trudinger and X. Wang, On the weak continuity of elliptic operators and applications to potential theory ,, Amer. Uhlenbeck, Regularity for a class of nonlinear elliptic systems ,, Acta Math. Zheng, Regualrity results for the generalized Beltrami systems ,, Acta Math. Sinica , 20 , Zheng, X. Zheng and Z. Feng, Regularity for a class of degenerate elliptic equations with discontinuous coefficients under natural growth ,, J.

Samia Challal , Abdeslem Lyaghfouri. Lucio Boccardo , Alessio Porretta. Lili Li , Chunrong Chen.

Journal of Modern Dynamics , , 6 1 : Jinpeng An. Atsushi Kawamoto. Luis Silvestre. Kyudong Choi. Luis Barreira , Claudia Valls. Rafael De La Llave , R. Luca Lorenzi. Vincent Lynch. Andrey Kochergin. Electronic Research Announcements , , Slobodan N. Sergey P. American Institute of Mathematical Sciences. In this paper we are concerned with a class of nonlinear degenerate elliptic equations under the natural growth. References: [1] E. Google Scholar [2] L. Google Scholar [3] E.