scholarly journals Regularity of solutions in semilinear elliptic theory

2016 ◽  
Vol 7 (1) ◽  
pp. 177-200 ◽  
Author(s):  
Emanuel Indrei ◽  
Andreas Minne ◽  
Levon Nurbekyan
Keyword(s):  
Regularity Of Solutions ◽  
Semilinear Elliptic ◽  
Elliptic Theory

scholarly journals Monotone iterations for nonlinear obstacle problem

1990 ◽  
Vol 31 (3) ◽  
pp. 259-276 ◽  
Author(s):  
Philip Korman ◽  
Anthony W. Leung ◽  
Srdjan Stojanovic
Keyword(s):  
Steady State ◽  
Partial Differential Equations ◽  
Population Model ◽  
Obstacle Problem ◽  
Elliptic Partial Differential Equations ◽  
Regularity Of Solutions ◽  
State Problem ◽  
Monotone Iterations ◽  
Semilinear Elliptic ◽  
Steady State Problem

AbstractThe existence, uniqueness and regularity of solutions are proved for the obstacle problem with semilinear elliptic partial differential equations of second order. Computationally effective algorithms are provided and application made to steady state problem for the logistic population model with diffusion and an obstacle to growth.

scholarly journals Semilinear elliptic Neumann problems with rapid growth in the nonlinearity

2006 ◽  
Vol 74 (2) ◽  
pp. 161-175 ◽  
Author(s):  
Jason R. Looker
Keyword(s):  
Weak Solution ◽  
Operator Theory ◽  
Existence And Uniqueness ◽  
Regularity Of Solutions ◽  
Pseudomonotone Operator ◽  
Neumann Problems ◽  
Semilinear Elliptic ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
Increasing Function

The existence and regularity of solutions to semilinear elliptic Neumann problems are investigated. Motivated by the Poisson–Boltzmann equation of biophysics and semiconductor modeling, the nonlinearity is assumed to be a continuous, strictly monotone increasing function that passes through the origin with asymptotically superlinear and unbounded growth. Pseudomonotone operator theory is utilised to establish the existence and uniqueness of a weak solution in the Sobolev space W1,2. With an additional assumption on the nonlinearity, we show that this weak solution belongs to .

scholarly journals Existence results for nonlinear degenerate elliptic equations with lower order terms

2020 ◽  
Vol 10 (1) ◽  
pp. 301-310
Author(s):  
Weilin Zou ◽  
Xinxin Li
Keyword(s):  
Lower Order ◽  
Elliptic Equations ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Regularity Of Solutions ◽  
Degenerate Elliptic Equations ◽  
Degenerate Elliptic ◽  
Initial Boundary Value ◽  
Lower Order Terms ◽  
Nonlinear Degenerate

Abstract In this paper, we prove the existence and regularity of solutions of the homogeneous Dirichlet initial-boundary value problem for a class of degenerate elliptic equations with lower order terms. The results we obtained here, extend some existing ones of [2, 9, 11] in some sense.

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