Geodesic
Integral estimates of solutions to boundary values problems for the Poisson equation
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2023), pp. 70-76.

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We consider solutions to two boundary values problems for the Poisson equation on plane domains. We prove several estimates for integrals of solutions using geometric characteristics of domains.
Mots-clés : Poisson equation
Keywords: Dirichlet problem, boundary values problem, isoperimetric inequality. 
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F. G. Avkhadiev; A. R. Kacimov. Integral estimates of solutions to boundary values problems for the Poisson equation. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2023), pp. 70-76. http://geodesic.mathdoc.fr/item/IVM_2023_10_a5/

[1] Strack O.D., “Three-Dimensional Streamlines in Dupuit-Forchheimer Models”, Water Resources Research, 20:7 (1984), 812–922 | DOI

[2] Strack O.D., Analytical Groundwater Mechanics, Cambridge Univ. Press, Cambridge, 2017 | MR

[3] Blunt M.J, Multiphase Flow in Permeable Media$:$ A Pore-Scale Perspective, Cambridge Univ. Press, Cambridge, 2017

[4] Shah R.K., London A.L., Laminar Flow Forced Convection in Ducts: a Source Book for Compact Heat Exchanger Analytical Data, Academic Press, New York, 1978

[5] Timoshenko S.P., History of Strength of Materials, McGraw-Hill, London, 1954 | Zbl

[6] Pólya G., Szegö G., Isoperimetric Inequalities in Mathematical Physics, Princeton Univ. Press, Princeton, 1951 | MR

[7] Bandle C., Isoperimetric Inequalities and Applications, Pitman Monographs and Studies in Math., 7, Boston, 1980 | MR | Zbl

[8] Avkhadiev F.G., Kacimov A.R., “Analytical Solutions and Estimates for Microlevel Flows”, J. Porous Media, 8:2 (2005), 125–148 | DOI

[9] Kacimov A.R., Obnosov Yu. V., “Profiling ponded soil surface in saturated seepage into drain-line sink: Kalashnikov's method of lateral leaching revisited”, European J. Appl. Math., 34:2 (2022), 367–384 | DOI | MR

[10] Avkhadiev F.G., Kacimov A.R., “The Saint-Venant type isoperimetric inequalities for assessing saturated water storage in lacunary shallow perched aquifers”, ZAMM, 103:1 (2023), 1–22 | DOI | MR

[11] Zaremba S., “Ob odnoi smeshannoi zadache, otnosyascheisya k uravneniyu Laplasa”, UMN, 1:3–4 (1946), 125–146 | Zbl

[12] Bitsadze A.V., Kraevye zadachi dlya ellipticheskikh uravnenii vtorogo poryadka, Nauka, M., 1966 | MR

[13] Avkhadiev F.G., “Reshenie obobschennoi zadachi Sen-Venana”, Matem. sb., 189:12 (1998), 3–12 | DOI | Zbl

[14] Bañuelos R., van den Berg M., Carroll T., “Torsional Rigidity and Expected Lifetime of Brownian Motion”, J. London Math. Soc., 66:2 (2002), 499–512 | DOI | MR

[15] Avkhadiev F. G., Salahudinov R. G., “Isoperimetric inequalities for conformal moments of plane domains”, J. Inequal. Appl., 7:4 (2002), 593–601 | MR | Zbl

[16] Avkhadiev F. G., Kayumov I. R., “Comparison theorems of isoperimetric type for moments of compact sets”, Collectanea Math., 55:1 (2004), 1–9 | MR | Zbl

[17] Avkhadiev F.G., “Novye izoperimetricheskie neravenstva dlya momentov oblastei i zhestkosti krucheniya”, Izv. vuzov. Matem., 2004, no. 7, 3–11 | Zbl

[18] Avkhadiev F.G., “Izoperimetricheskoe neravenstvo dlya zhestkosti krucheniya v mnogomernykh oblastyakh”, Izv. vuzov. Matem., 2012, no. 7, 45–49 | Zbl

[19] Avkhadiev F.G., “Teoremy vlozheniya, svyazannye s zhestkostyu krucheniya i osnovnoi chastotoi”, Izv. RAN. Ser. matem., 86:1 (2022), 3–35 | DOI | MR | Zbl

[20] Apushkinskaya D.E., Nazarov A.I., “Lemma o normalnoi proizvodnoi i vokrug nee”, UMN, 77:2 (2022), 3–68 | DOI | MR | Zbl