On the KPZ equation with fractional diffusion: Global regularity and existence results
暂无分享,去创建一个
Fernando Soria | Boumediene Abdellaoui | Ireneo Peral | Ana Primo | F. Soria | B. Abdellaoui | I. Peral | A. Primo
[1] R. Durán,et al. Weighted a priori estimates for the Poisson equation , 2008 .
[2] Ivan Corwin. The Kardar-Parisi-Zhang equation and universality class , 2011, 1106.1596.
[3] L. Véron,et al. Semilinear fractional elliptic equations with gradient nonlinearity involving measures , 2013, 1308.6720.
[4] Wojbor A. Woyczyński,et al. Critical nonlinearity exponent and self-similar asymptotics for Lévy conservation laws , 2001 .
[5] B. Abdellaoui,et al. On fractional p-Laplacian parabolic problem with general data , 2016, 1612.01301.
[6] Tommaso Leonori,et al. Basic estimates for solutions of a class of nonlocal elliptic and parabolic equations , 2015 .
[7] Yvan Martel,et al. Complete blow up and global behaviour of solutions of ut - Δu = g(u) , 1998 .
[8] Alessio Figalli,et al. Regularity of solutions to the parabolic fractional obstacle problem , 2011, 1101.5170.
[9] Wojbor A. Woyczyński,et al. Fractal Hamilton-Jacobi-KPZ equations , 2006 .
[10] Xavier Ros-Oton,et al. The Dirichlet problem for the fractional Laplacian: Regularity up to the boundary , 2012, 1207.5985.
[11] B. Gilding. The Cauchy problem for ut=?u+|?u|qut=?u+|?u|q, large-time behaviour , 2003 .
[12] D. Applebaum. Lévy Processes and Stochastic Calculus: Preface , 2009 .
[13] J. Droniou,et al. Fractal First-Order Partial Differential Equations , 2006 .
[14] E. Valdinoci,et al. Hitchhiker's guide to the fractional Sobolev spaces , 2011, 1104.4345.
[15] Wojbor A. Woyczyński,et al. Burgers-KPZ turbulence : Göttingen lectures , 1998 .
[16] Krzysztof Bogdan,et al. Estimates of the Green Function for the Fractional Laplacian Perturbed by Gradient , 2010, 1009.2472.
[17] L. Véron,et al. Semilinear fractional elliptic equations involving measures , 2013, 1305.0945.
[18] Zhang,et al. Dynamic scaling of growing interfaces. , 1986, Physical review letters.
[19] G. I. Barenblatt,et al. Self-similar intermediate asymptotics for a degenerate parabolic filtration-absorption equation. , 2000, Proceedings of the National Academy of Sciences of the United States of America.
[20] R. Song,et al. Dirichlet Heat Kernel Estimates for Stable Processes with Singular Drift In Unbounded C1,1 Open Sets , 2014 .
[21] Martin Hairer. Solving the KPZ equation , 2011, 1109.6811.
[22] Zhen-Qing Chen,et al. Dirichlet heat kernel estimates for fractional Laplacian with gradient perturbation , 2010, 1011.3273.
[23] Tomasz Jakubowski,et al. Time-dependent gradient perturbations of fractional Laplacian , 2010 .
[24] A. Dall'Aglio,et al. Regularity and nonuniqueness results for parabolic problems arising in some physical models, having natural growth in the gradient , 2008 .
[25] T. Gallouët,et al. Non-linear elliptic and parabolic equations involving measure data , 1989 .
[26] N. Laskin. Fractional quantum mechanics and Lévy path integrals , 1999, hep-ph/9910419.
[27] G. Vojta,et al. Fractal Concepts in Surface Growth , 1996 .
[28] P. Alam. ‘A’ , 2021, Composites Engineering: An A–Z Guide.
[29] W. A. Woyczyński. Burgers-KPZ Turbulence , 1998 .
[30] Strong Regularizing Effect of a Gradient Term in the Heat Equation with a Weight , 2013 .
[31] A. Dall'Aglio,et al. Global Existence for Nonlinear Parabolic Problems With Measure Data– Applications to Non-uniqueness for Parabolic Problems With Critical Gradient terms , 2011 .
[32] Daniel B. Henry. Geometric Theory of Semilinear Parabolic Equations , 1989 .
[33] R. Stephenson. A and V , 1962, The British journal of ophthalmology.
[34] N. S. Landkof. Foundations of Modern Potential Theory , 1972 .
[35] F. Weissler,et al. The local theory for viscous Hamilton–Jacobi equations in Lebesgue spaces , 2002 .
[36] Juha Lehrbäck. Weighted Hardy inequalities and the size of the boundary , 2008 .
[37] Enrique Zuazua,et al. Local regularity for fractional heat equations , 2017, 1704.07562.
[38] N. Alaa. Solutions faibles d'équations paraboliques quasilinéaires avec données initiales mesurés , 1996 .
[39] B. Barrios,et al. Strong maximum principles for fractional elliptic and parabolic problems with mixed boundary conditions , 2016, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.
[40] M. Surnachev. Density of smooth functions in weighted Sobolev spaces with variable exponent , 2014, Doklady Mathematics.
[41] Ireneo Peral Alonso,et al. Elliptic and Parabolic Equations Involving the Hardy-Leray Potential , 2021 .
[42] G. Burton. Sobolev Spaces , 2013 .
[43] E. Valdinoci,et al. Dislocation Dynamics in Crystals: A Macroscopic Theory in a Fractional Laplace Setting , 2013 .
[45] G. Grubb. Regularity in $L_p$ Sobolev spaces of solutions to fractional heat equations , 2017, 1706.06058.
[46] N. Phuc. Morrey global bounds and quasilinear Riccati type equations below the natural exponent , 2014 .
[47] Tsuyoshi Murata,et al. {m , 1934, ACML.
[48] Adimurthi,et al. Positive solutions to a fractional equation with singular nonlinearity , 2017, Journal of Differential Equations.
[49] N. Phuc,et al. Quasilinear Riccati type equations with distributional data in Morrey space framework , 2016 .
[50] Marcel Riesz,et al. Integrales de Riemann-Liouville et Potentiels , 1988 .
[51] Nicola Abatangelo. Large $s$-harmonic functions and boundary blow-up solutions for the fractional Laplacian , 2013, 1310.3193.
[52] P. Alam. ‘G’ , 2021, Composites Engineering: An A–Z Guide.
[53] B. Abdellaoui,et al. Some existence and regularity results for porous media and fast diffusion equations with a gradient term , 2012, 1210.5062.
[54] Strongly Nonlocal Dislocation Dynamics in Crystals , 2013, 1311.3549.