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- Juan Luis Vázquez

Mathematics

Spain

2023

Discipline name
D-index
D-index (Discipline H-index) only includes papers and citation values for an examined
discipline in contrast to General H-index which accounts for publications across all
disciplines.
Citations
Publications
World Ranking
National Ranking

Mathematics
D-index
69
Citations
19,707
334
World Ranking
212
National Ranking
3

2023 - Research.com Mathematics in Spain Leader Award

2022 - Research.com Mathematics in Spain Leader Award

2016 - Member of the European Academy of Sciences

2013 - Fellow of the American Mathematical Society

- Mathematical analysis
- Quantum mechanics
- Partial differential equation

His main research concerns Mathematical analysis, Nonlinear system, Heat equation, Porous medium and Uniqueness. He combines subjects such as Inverse and Diffusion equation with his study of Mathematical analysis. His research in Nonlinear system intersects with topics in Semigroup, Elliptic curve, Algebra, Thermal diffusivity and Space.

His studies in Heat equation integrate themes in fields like Initial value problem, Simultaneous equations, Sign, Statistical physics and Independent equation. His Uniqueness research is multidisciplinary, incorporating elements of Mathematical proof, Combinatorics, Type, Symmetry in biology and Weak solution. His Bounded function research is multidisciplinary, incorporating perspectives in Nonlinear heat equation, Function space, Pure mathematics and Domain.

- A Strong Maximum Principle for some quasilinear elliptic equations (927 citations)
- An $L^1$ -theory of existence and uniqueness of solutions of nonlinear elliptic equations (737 citations)
- The Porous Medium Equation: Mathematical Theory (612 citations)

The scientist’s investigation covers issues in Mathematical analysis, Bounded function, Nonlinear system, Porous medium and Heat equation. His Diffusion equation research extends to Mathematical analysis, which is thematically connected. His study in Bounded function is interdisciplinary in nature, drawing from both Pure mathematics, Mathematical physics, Dirichlet problem, Boundary value problem and Domain.

Juan Luis Vázquez has included themes like p-Laplacian and Laplace operator in his Pure mathematics study. The Domain study combines topics in areas such as Zero and Dirichlet boundary condition. His study on Nonlinear system also encompasses disciplines like

- Type that intertwine with fields like Limit,
- Degenerate energy levels which is related to area like Parabolic partial differential equation.

- Mathematical analysis (70.75%)
- Bounded function (25.00%)
- Nonlinear system (22.25%)

- Mathematical analysis (70.75%)
- Bounded function (25.00%)
- Pure mathematics (14.00%)

Mathematical analysis, Bounded function, Pure mathematics, Nonlinear system and Space are his primary areas of study. In his works, Juan Luis Vázquez performs multidisciplinary study on Mathematical analysis and Porous medium. His work carried out in the field of Bounded function brings together such families of science as Boundary value problem, Dirichlet conditions, Uniqueness, Domain and Laplace operator.

His Pure mathematics study combines topics in areas such as p-Laplacian and Scalar curvature. His studies deal with areas such as Order, Logarithm, Statistical physics, Exponential function and Degenerate energy levels as well as Nonlinear system. His Space study also includes

- Constant and related Function space, Sobolev space and Combinatorics,
- Nabla symbol that intertwine with fields like Compact space, Inverse, Balanced flow, Vortex and Viscosity solution.

- Optimal existence and uniqueness theory for the fractional heat equation (54 citations)
- The Mathematical Theories of Diffusion: Nonlinear and Fractional Diffusion (50 citations)
- Sharp boundary behaviour of solutions to semilinear nonlocal elliptic equations (39 citations)

- Mathematical analysis
- Quantum mechanics
- Geometry

Juan Luis Vázquez mainly investigates Bounded function, Mathematical analysis, Pure mathematics, Domain and Nonlinear system. The concepts of his Bounded function study are interwoven with issues in Omega, Measure, Dirichlet conditions, Uniqueness and Degenerate energy levels. Juan Luis Vázquez merges Mathematical analysis with Porous medium in his study.

His work deals with themes such as Smoothness and Laplace operator, which intersect with Pure mathematics. His Domain research is multidisciplinary, incorporating perspectives in Zero and Fractional Laplacian. He has researched Nonlinear system in several fields, including Dimension, Mathematical physics, Logarithmic scale, Fractional diffusion and Sigma.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

The Porous Medium Equation: Mathematical Theory

Juan Luis Vázquez.

**(2006)**

1840 Citations

A Strong Maximum Principle for some quasilinear elliptic equations

J. L. Vázquez.

Applied Mathematics and Optimization **(1984)**

1338 Citations

An $L^1$ -theory of existence and uniqueness of solutions of nonlinear elliptic equations

Philippe Bénilan;Lucio Boccardo;Thierry Gallouët;Ron Gariepy.

Annali Della Scuola Normale Superiore Di Pisa-classe Di Scienze **(1995)**

1209 Citations

The Porous Medium Equation

Juan Luis Vazquez.

**(2006)**

956 Citations

Blow-up solutions of some nonlinear elliptic problems

Haim Brezis;Juan Luis Vázquez.

Revista Matematica Complutense **(1997)**

711 Citations

Smoothing and decay estimates for nonlinear diffusion equations : equations of porous medium type

Juan Luis Vázquez.

**(2006)**

498 Citations

The problem of blow-up in nonlinear parabolic equations

Victor A. Galaktionov;Juan-Luis Vázquez.

Discrete and Continuous Dynamical Systems **(2002)**

475 Citations

The Hardy Inequality and the Asymptotic Behaviour of the Heat Equation with an Inverse-Square Potential

Juan Luis Vazquez;Enrike Zuazua.

Journal of Functional Analysis **(2000)**

465 Citations

Smoothing and Decay Estimates for Nonlinear Diffusion Equations

Juan Luis Vázquez.

**(2006)**

388 Citations

Continuation of blowup solutions of nonlinear heat equations in several space dimensions

Victor A. Galaktionov;Juan L. Vazquez.

Communications on Pure and Applied Mathematics **(1997)**

386 Citations

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