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Some remarks on the $L^p-L^q$ boundedness of trigonometric sums and oscillatory integrals
On certain nonlinear parabolic equations with singular diffusion and data in $L^1$
1. | Departamento de Matemáticas, Universidad de Cádiz, CASEM, Campus del Río San Pedro, 11510 Puerto Real, Cádiz, Spain, Spain |
[1] |
Zhigang Wang, Lei Wang, Yachun Li. Renormalized entropy solutions for degenerate parabolic-hyperbolic equations with time-space dependent coefficients. Communications on Pure and Applied Analysis, 2013, 12 (3) : 1163-1182. doi: 10.3934/cpaa.2013.12.1163 |
[2] |
Alberto Fiorenza, Anna Mercaldo, Jean Michel Rakotoson. Regularity and uniqueness results in grand Sobolev spaces for parabolic equations with measure data. Discrete and Continuous Dynamical Systems, 2002, 8 (4) : 893-906. doi: 10.3934/dcds.2002.8.893 |
[3] |
Valerii Los, Vladimir Mikhailets, Aleksandr Murach. Parabolic problems in generalized Sobolev spaces. Communications on Pure and Applied Analysis, 2021, 20 (10) : 3605-3636. doi: 10.3934/cpaa.2021123 |
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Qiang Liu, Zhichang Guo, Chunpeng Wang. Renormalized solutions to a reaction-diffusion system applied to image denoising. Discrete and Continuous Dynamical Systems - B, 2016, 21 (6) : 1839-1858. doi: 10.3934/dcdsb.2016025 |
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Luisa Moschini, Guillermo Reyes, Alberto Tesei. Nonuniqueness of solutions to semilinear parabolic equations with singular coefficients. Communications on Pure and Applied Analysis, 2006, 5 (1) : 155-179. doi: 10.3934/cpaa.2006.5.155 |
[6] |
Gary Lieberman. A new regularity estimate for solutions of singular parabolic equations. Conference Publications, 2005, 2005 (Special) : 605-610. doi: 10.3934/proc.2005.2005.605 |
[7] |
Xiaomei Sun, Wenyi Chen. Positive solutions for singular elliptic equations with critical Hardy-Sobolev exponent. Communications on Pure and Applied Analysis, 2011, 10 (2) : 527-540. doi: 10.3934/cpaa.2011.10.527 |
[8] |
Stephen Pankavich, Petronela Radu. Nonlinear instability of solutions in parabolic and hyperbolic diffusion. Evolution Equations and Control Theory, 2013, 2 (2) : 403-422. doi: 10.3934/eect.2013.2.403 |
[9] |
Doyoon Kim, Kyeong-Hun Kim, Kijung Lee. Parabolic Systems with measurable coefficients in weighted Sobolev spaces. Communications on Pure and Applied Analysis, , () : -. doi: 10.3934/cpaa.2022062 |
[10] |
Doyoon Kim, Hongjie Dong, Hong Zhang. Neumann problem for non-divergence elliptic and parabolic equations with BMO$_x$ coefficients in weighted Sobolev spaces. Discrete and Continuous Dynamical Systems, 2016, 36 (9) : 4895-4914. doi: 10.3934/dcds.2016011 |
[11] |
Peter Weidemaier. Maximal regularity for parabolic equations with inhomogeneous boundary conditions in Sobolev spaces with mixed $L_p$-norm. Electronic Research Announcements, 2002, 8: 47-51. |
[12] |
Simona Fornaro, Maria Sosio, Vincenzo Vespri. Harnack type inequalities for some doubly nonlinear singular parabolic equations. Discrete and Continuous Dynamical Systems, 2015, 35 (12) : 5909-5926. doi: 10.3934/dcds.2015.35.5909 |
[13] |
Mostafa Bendahmane, Kenneth H. Karlsen. Renormalized solutions of an anisotropic reaction-diffusion-advection system with $L^1$ data. Communications on Pure and Applied Analysis, 2006, 5 (4) : 733-762. doi: 10.3934/cpaa.2006.5.733 |
[14] |
Vitali Liskevich, Igor I. Skrypnik. Pointwise estimates for solutions of singular quasi-linear parabolic equations. Discrete and Continuous Dynamical Systems - S, 2013, 6 (4) : 1029-1042. doi: 10.3934/dcdss.2013.6.1029 |
[15] |
Jann-Long Chern, Yong-Li Tang, Chuan-Jen Chyan, Yi-Jung Chen. On the uniqueness of singular solutions for a Hardy-Sobolev equation. Conference Publications, 2013, 2013 (special) : 123-128. doi: 10.3934/proc.2013.2013.123 |
[16] |
Younghun Hong, Yannick Sire. On Fractional Schrödinger Equations in sobolev spaces. Communications on Pure and Applied Analysis, 2015, 14 (6) : 2265-2282. doi: 10.3934/cpaa.2015.14.2265 |
[17] |
Khalid Latrach, Hssaine Oummi, Ahmed Zeghal. Existence results for nonlinear mono-energetic singular transport equations: $ L^p $-spaces. Discrete and Continuous Dynamical Systems - S, 2022, 15 (1) : 179-195. doi: 10.3934/dcdss.2021028 |
[18] |
Xiying Sun, Qihuai Liu, Dingbian Qian, Na Zhao. Infinitely many subharmonic solutions for nonlinear equations with singular $ \phi $-Laplacian. Communications on Pure and Applied Analysis, 2020, 19 (1) : 279-292. doi: 10.3934/cpaa.20200015 |
[19] |
Françoise Demengel, O. Goubet. Existence of boundary blow up solutions for singular or degenerate fully nonlinear equations. Communications on Pure and Applied Analysis, 2013, 12 (2) : 621-645. doi: 10.3934/cpaa.2013.12.621 |
[20] |
Peiying Chen. Existence and uniqueness of weak solutions for a class of nonlinear parabolic equations. Electronic Research Announcements, 2017, 24: 38-52. doi: 10.3934/era.2017.24.005 |
2020 Impact Factor: 1.916
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